Výpis publikací

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN. Oscillation theory on hybrid time domains: Local oscillation properties. Journal of Differential Equations. Elsevier Inc, 2026, roč. 457, March, s. 114080-114121. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2025.114080.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory. Applied Mathematics in Science and Engineering. Taylor & Francis Ltd, 2025, roč. 33, č. 1, s. 1-39. ISSN 2769-0911. Dostupné z: https://doi.org/10.1080/27690911.2025.2494577.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. New existence results for conjoined bases of singular linear Hamiltonian systems with given Sturmian properties. Linear Algebra and its Applications. Elsevier, 2025, roč. 707, February, s. 187-224. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2024.11.017.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Contributions to Generalized Oscillation Theory of Linear Hamiltonian Systems. Results in Mathematics. Springer Nature, 2024, roč. 79, č. 8, s. 1-47. ISSN 1422-6383. Dostupné z: https://doi.org/10.1007/s00025-024-02280-7.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Note on singular Sturm comparison theorem and strict majorant condition. Journal of Mathematical Analysis and Applications. Elsevier, 2024, roč. 538, č. 2, s. 1-16. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2024.128391.

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER. Comparative index and Hörmander index in finite dimension and their connections. Filomat. Faculty of Sciences and Mathematics, University of Nis, 2023, roč. 37, č. 16, s. 5243-5257. ISSN 0354-5180. Dostupné z: https://doi.org/10.2298/FIL2316243E.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Generalized focal points and local Sturmian theory for linear Hamiltonian systems. Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences, 2023, roč. 43, č. 12, s. 4139-4173. ISSN 1078-0947. Dostupné z: https://doi.org/10.3934/dcds.2023082.

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER. Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index. Journal of Dynamics and Differential Equations. Springer, 2023, roč. 35, č. 3, s. 2589-2620. ISSN 1040-7294. Dostupné z: https://doi.org/10.1007/s10884-022-10140-7.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems. Monatshefte für Mathematik. Springer, 2023, roč. 200, č. 2, s. 359-387. ISSN 0026-9255. Dostupné z: https://doi.org/10.1007/s00605-022-01780-4.

BARTONIČKA, Tomáš; Zdeněk BOCHNÍČEK; Vítězslav BRYJA; Petr BUREŠ; Magdalena BURGR; Martin CULEK; Miloš ČERNÍK; Martin ČERNOHORSKÝ; Dominik ČERNÝ; Martin ČUTA; Jiří DANIHELKA; Jiří DOŠKAŘ; Zuzana DOŠLÁ; Petr FIRBAS; Eduard FUCHS; Milan GELNAR; Jan GLOSER; Michal HÁJEK; Jan HELEŠIC; Ivan HOLOUBEK; Michal HORSÁK; Petr HROUDA; Dagmar CHYTKOVÁ; Magdaléna CHYTRÁ; Milan CHYTRÝ; Zuzana JAYASUNDERA; Jaroslav JONAS; Mikoláš JURDA; Josef KALAS; Tomáš KAŠPAROVSKÝ; Jana KLÁNOVÁ; Jaroslav KOČA; Alois KOZUBÍK; František KUBÍČEK; Radan KUČERA; Aleš LACINA; Kamil LÁSKA; Jaromír LEICHMANN; Zdeněk LOSOS; Přemysl LUBAL; Jaroslav MALINA; Petr MIKULÍK; Dominik MUNZAR; Rudolf MUSIL; Jana MUSILOVÁ; Marek NEČAS; Miroslav NĚMEC; Milan NOVÁK; Kateřina NOVÁKOVÁ; Stanislav PEKÁR; Milan POTÁČEK; Pavel PROŠEK; Antonín PŘICHYSTAL; Jiřina RELICHOVÁ; Jiří ROSICKÝ; Zdeněk ŘEHÁK; Ivo SEDLÁČEK; Jana SCHENKOVÁ; Jiří SCHLAGHAMERSKÝ; Eduard SCHMIDT; Pavlína SLAVÍKOVÁ; Jan SLOVÁK; Josef STANĚK; Kateřina ŠEBKOVÁ; Vladimír ŠIMEK; Roman ŠIMON HILSCHER; Pavel ŠIŠMA; Taťána ŠKARKOVÁ; Petr ŠPAČEK; Magdalena ŠPOKOVÁ; Vladimír ŠTEFL; Jan ŠVANCARA; Andrea ŠPALEK TÓTHOVÁ; Libuše TRNKOVÁ; David TRUNEC; Martin VÁCHA; Jaromír VAŇHARA; Monika VÍTĚZOVÁ; Michaela WIMMEROVÁ; Světlana ZAHRÁDKOVÁ; Petr ZBOŘIL a Josef ZEMAN. Dějiny psané přírodovědci : Vývoj vědních oborů na Přírodovědecké fakultě Masarykovy univerzity. Online. Edited by Milan Gelnar - Z. Jayasundera. 1., elektronické vyd. Brno: Masarykova univerzita, 2022, 997 s. ISBN 978-80-280-0089-9.

BARTONIČKA, Tomáš; Zdeněk BOCHNÍČEK; Vítězslav BRYJA; Petr BUREŠ; Magdalena BURGR; Martin CULEK; Miloš ČERNÍK; Martin ČERNOHORSKÝ; Dominik ČERNÝ; Martin ČUTA; Jiří DANIHELKA; Jiří DOŠKAŘ; Zuzana DOŠLÁ; Petr FIRBAS; Eduard FUCHS; Milan GELNAR; Jan GLOSER; Michal HÁJEK; Jan HELEŠIC; Ivan HOLOUBEK; Michal HORSÁK; Petr HROUDA; Dagmar CHYTKOVÁ; Magdaléna CHYTRÁ; Milan CHYTRÝ; Zuzana JAYASUNDERA; Jaroslav JONAS; Mikoláš JURDA; Josef KALAS; Tomáš KAŠPAROVSKÝ; Jana KLÁNOVÁ; Jaroslav KOČA; Alois KOZUBÍK; František KUBÍČEK; Radan KUČERA; Aleš LACINA; Kamil LÁSKA; Jaromír LEICHMANN; Zdeněk LOSOS; Přemysl LUBAL; Jaroslav MALINA; Petr MIKULÍK; Dominik MUNZAR; Rudolf MUSIL; Jana MUSILOVÁ; Marek NEČAS; Miroslav NĚMEC; Milan NOVÁK; Kateřina NOVÁKOVÁ; Stanislav PEKÁR; Milan POTÁČEK; Pavel PROŠEK; Antonín PŘICHYSTAL; Jiřina RELICHOVÁ; Jiří ROSICKÝ; Zdeněk ŘEHÁK; Ivo SEDLÁČEK; Jana SCHENKOVÁ; Jiří SCHLAGHAMERSKÝ; Eduard SCHMIDT; Pavlína SLAVÍKOVÁ; Jan SLOVÁK; Josef STANĚK; Kateřina ŠEBKOVÁ; Vladimír ŠIMEK; Roman ŠIMON HILSCHER; Pavel ŠIŠMA; Taťána ŠKARKOVÁ; Petr ŠPAČEK; Magdalena ŠPOKOVÁ; Vladimír ŠTEFL; Jan ŠVANCARA; Andrea ŠPALEK TÓTHOVÁ; Libuše TRNKOVÁ; David TRUNEC; Martin VÁCHA; Jaromír VAŇHARA; Monika VÍTĚZOVÁ; Michaela WIMMEROVÁ; Světlana ZAHRÁDKOVÁ; Petr ZBOŘIL a Josef ZEMAN. Dějiny psané přírodovědci : Vývoj vědních oborů na Přírodovědecké fakultě Masarykovy univerzity. Edited by Milan Gelnar - Z. Jayasundera. 1. vyd. Brno: Masarykova univerzita, 2022, 997 s. ISBN 978-80-280-0088-2.

ŘEHÁK, Pavel a Roman ŠIMON HILSCHER. EQUADIFF 15. History, Personalities, Plenary and Invited Abstracts, and Program. 1., elektronické vyd. Brno: Masarykova univerzita, 2022, 110 s. ISBN 978-80-280-0239-8.

ŘEHÁK, Pavel a Roman ŠIMON HILSCHER. EQUADIFF 15. History, Personalities, Plenary and Invited Abstracts, and Program. 1. vyd. Brno: Masarykova univerzita, 2022, 110 s. ISBN 978-80-280-0082-0.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems. Annali di Matematica Pura ed Applicata. Springer, 2022, roč. 201, č. 5, s. 2121-2136. ISSN 0373-3114. Dostupné z: https://doi.org/10.1007/s10231-022-01194-x.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Comparative index and Lidskii angles for symplectic matrices. Linear Algebra and its Applications. Elsevier, 2021, roč. 624, September, s. 174-197. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2021.04.012.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Distribution and number of focal points for linear Hamiltonian systems. Linear Algebra and Its Applications. Elsevier, 2021, roč. 611, February 2021, s. 26-45. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2020.11.018.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Journal of Differential Equations. Elsevier, 2021, roč. 298, October, s. 1-29. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2021.06.037.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations. EDP Sciences, 2021, roč. 27, July, s. "75", 35 s. ISSN 1292-8119. Dostupné z: https://doi.org/10.1051/cocv/2021068.

DŘÍMALOVÁ, Iva a Roman ŠIMON HILSCHER. Antiprincipal solutions at infinity for symplectic systems on time scales. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: University of Szeged, 2020, Neuveden, č. 44, s. 1-32. ISSN 1417-3875. Dostupné z: https://doi.org/10.14232/ejqtde.2020.1.44.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Singular Sturmian comparison theorems for linear Hamiltonian systems. Journal of Differential Equations. Amsterdam: Elsevier, 2020, roč. 269, č. 4, s. 2920-2955. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2020.02.016.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. Journal of Mathematical Analysis and Applications. San Diego: Elsevier, 2020, roč. 487, č. 2, s. 1-14. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2020.124030.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Journal of Differential Equations. San Diego: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2019, roč. 266, č. 11, s. 7481-7524. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2018.12.007.

DOŠLÝ, Ondřej; Julia ELYSEEVA a Roman ŠIMON HILSCHER. Symplectic Difference Systems: Oscillation and Spectral Theory. Cham: Birkhäuser/Springer, 2019, 593 s. Pathways in Mathematics. ISBN 978-3-030-19372-0. Dostupné z: https://doi.org/10.1007/978-3-030-19373-7.

ELYSEEVA, Julia a Roman ŠIMON HILSCHER. Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter. Linear Algebra and Its Applications. Elsevier, 2018, roč. 558, 1 December 2018, s. 108-145. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2018.08.013.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Focal points and principal solutions of linear Hamiltonian systems revisited. Journal of Differential Equations. Amsterdam: Elsevier, 2018, roč. 264, č. 9, s. 5541-5576. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2018.01.016.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems. Annali di Matematica Pura ed Applicata. Series IV. Berlin: Springer, 2018, roč. 197, č. 1, s. 283-306. ISSN 0373-3114. Dostupné z: https://doi.org/10.1007/s10231-017-0679-7.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Singular Sturmian separation theorems for nonoscillatory symplectic difference systems. Journal of Difference Equations and Applications. Abingdon: Taylor & Francis, 2018, roč. 24, č. 12, s. 1894-1934. ISSN 1023-6198. Dostupné z: https://doi.org/10.1080/10236198.2018.1544247.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. ESAIM: Control, Optimisation and Calculus of Variations. Les Ulis: E D P Sciences, 2018, roč. 24, č. 4, s. 1705-1734. ISSN 1292-8119. Dostupné z: https://doi.org/10.1051/cocv/2017070.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Comparative index and Sturmian theory for linear Hamiltonian systems. Journal of Differential Equations. San Diego, CA USA: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, roč. 262, č. 2, s. 914-944. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2016.09.043.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Journal of Difference Equations and Applications. ABINGDON, ENGLAND: Taylor and Francis, 2017, roč. 23, č. 4, s. 657-698. ISSN 1023-6198. Dostupné z: https://doi.org/10.1080/10236198.2016.1270274.

DŘÍMALOVÁ, Iva; Werner KRATZ a Roman ŠIMON HILSCHER. Sturm-Liouville matrix differential systems with singular leading coefficient. Annali di Matematica Pura ed Applicata. Series IV. HEIDELBERG: Springer HEIDELBERG, 2017, roč. 196, č. 3, s. 1165-1183. ISSN 0373-3114. Dostupné z: https://doi.org/10.1007/s10231-016-0611-6.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity. Journal of Differential Equations. Elsevier, 2016, roč. 260, č. 8, s. 6581-6603. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2016.01.004.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Principal solutions at infinity for time scale symplectic systems without controllability condition. Journal of Mathematical Analysis and Applications. Elsevier, 2016, roč. 444, č. 2, s. 852-880. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2016.06.057.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems. In S. Pinelas, Z. Došlá, O. Došlý, P.E. Kloeden. Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. NEW YORK: Springer, 2016, s. 359-369. ISBN 978-3-319-32855-3. Dostupné z: https://doi.org/10.1007/978-3-319-32857-7_34.

ŠIMON HILSCHER, Roman. Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: Electronic Journal of Qualitative Theory of Differential Equations, Bolyai Institute, University of Szeged, 2015, roč. 54, č. 54, s. "nestrankovano", 16 s. ISSN 1417-3875.

ŠIMON HILSCHER, Roman. Eigenvalue comparison for discrete symplectic systems. In M. Bohner, Y. Ding, O. Došlý. Difference Equations, Discrete Dynamical Systems and Applications. Berlin: Springer, 2015, s. 95-107. ISBN 978-3-319-24745-8.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Limit circle invariance for two differential systems on time scales. Mathematische Nachrichten. Akademie-Verlag, 2015, roč. 288, 5-6, s. 696-709. ISSN 0025-584X. Dostupné z: https://doi.org/10.1002/mana.201400005.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Journal of Differential Equations. Elsevier, 2015, roč. 259, č. 9, s. 4651-4682. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2015.06.027.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Journal of Dynamics and Differential Equations. New York: Springer, 2015, roč. 27, č. 1, s. 137-175. ISSN 1040-7294. Dostupné z: https://doi.org/10.1007/s10884-014-9389-7.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Recessive solutions for nonoscillatory discrete symplectic systems. Linear Algebra and Its Applications. Elsevier, 2015, roč. 469, March, s. 243-275. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2014.11.029.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Time scale symplectic systems with analytic dependence on spectral parameter. Journal of Difference Equations and Applications. London: Taylor and Francis, 2015, roč. 21, č. 3, s. 209-239. ISSN 1023-6198. Dostupné z: https://doi.org/10.1080/10236198.2014.997227.

ŠIMON HILSCHER, Roman. Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Mathematische Nachrichten. Wiley Inter Science, 2014, roč. 287, 5-6, s. 704-716. ISSN 0025-584X. Dostupné z: https://doi.org/10.1002/mana.201200314.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. In Z. AlSharawi, J. Cushing, S. Elaydi. Theory and Applications of Difference Equations and Discrete Dynamical Systems. Berlin: Springer, 2014, s. 187-202. ISBN 978-3-662-44139-8. Dostupné z: https://doi.org/10.1007/978-3-662-44140-4_10.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Limit point and limit circle classification for symplectic systems on time scales. Applied Mathematics and Computation. Spojené státy americké: Elsevier, 2014, roč. 233, MAY, s. 623-646. ISSN 0096-3003. Dostupné z: https://doi.org/10.1016/j.amc.2013.12.135.

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Journal of Dynamics and Differential Equations. New York: Springer, 2014, roč. 26, č. 1, s. 57-91. ISSN 1040-7294. Dostupné z: https://doi.org/10.1007/s10884-013-9342-1.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Journal of Difference Equations and Applications. Taylor and Francis, 2014, roč. 20, č. 1, s. 84-117. ISSN 1023-6198. Dostupné z: https://doi.org/10.1080/10236198.2013.813496.

KRATZ, Werner a Roman ŠIMON HILSCHER. A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. SIAM Journal on Matrix Analysis and Applications. Philadelphia, PA, USA: SIAM, 2013, roč. 34, č. 1, s. 228-243. ISSN 0895-4798. Dostupné z: https://doi.org/10.1137/120873029.

ŠIMON HILSCHER, Roman. Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 2013, roč. 22, č. 1, s. 115-124. ISSN 1056-2176.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Advances in Difference Equations. Berlín: Springer, 2013, roč. 2013, č. 232, s. 1-18. ISSN 1687-1847. Dostupné z: https://doi.org/10.1186/1687-1847-2013-232.

ŠIMON HILSCHER, Roman. Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Applied Mathematics and Computation. Spojené státy americké: Elsevier, 2012, roč. 219, č. 6, s. 2839-2860. ISSN 0096-3003. Dostupné z: https://doi.org/10.1016/j.amc.2012.08.026.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Nonlinear Analysis, Theory, Methods & Applications. Amsterdam: Elsevier Science Ltd., 2012, roč. 75, č. 2, s. 932-950. ISSN 0362-546X. Dostupné z: https://doi.org/10.1016/j.na.2011.09.027.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. New results for time reversed symplectic dynamic systems and quadratic functionals. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, University of Szeged, 2012, Neuveden, č. 15, s. 1-11. ISSN 1417-3875.

BOHNER, Martin; Werner KRATZ a Roman ŠIMON HILSCHER. Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter. Mathematische Nachrichten. Wiley Inter Science, 2012, roč. 285, 11-12, s. 1343-1356. ISSN 0025-584X. Dostupné z: https://doi.org/10.1002/mana.201100172.

DOŠLÝ, Ondřej; Abdullah ÖZBEKLER a Roman ŠIMON HILSCHER. Oscillation criterion for half-linear differential equations with periodic coefficients. Journal of Mathematical Analysis and Applications. San Diego (USA): Elsevier Science, 2012, roč. 393, č. 2, s. 360-366. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2012.03.020.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Applied Mathematics and Computation. Spojené státy americké: Elsevier, 2012, roč. 218, č. 17, s. 8309-8328. ISSN 0096-3003. Dostupné z: https://doi.org/10.1016/j.amc.2012.01.056.

ŠIMON HILSCHER, Roman. Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Linear Algebra and Its Applications. Elsevier, 2012, roč. 437, č. 12, s. 2922-2960. ISSN 0024-3795. Dostupné z: https://doi.org/10.1016/j.laa.2012.06.033.

KRATZ, Werner a Roman ŠIMON HILSCHER. Rayleigh principle for linear Hamiltonian systems without controllability. ESAIM: Control, Optimisation and Calculus of Variations. Les Ulis: EDP Sciences, 2012, roč. 18, č. 2, s. 501-519. ISSN 1292-8119. Dostupné z: https://doi.org/10.1051/cocv/2011104.

ŠIMON HILSCHER, Roman. Spectral and oscillation theory for general second order Sturm-Liouville difference equations. Advances in Difference Equations. Springer, 2012, roč. 2012, č. 82, s. 1-19. ISSN 1687-1847. Dostupné z: https://doi.org/10.1186/1687-1847-2012-82.

KRATZ, Werner; Roman ŠIMON HILSCHER a Vera Michel ZEIDAN. Eigenvalue and oscillation theorems for time scale symplectic systems. International Journal of Dynamical Systems and Differential Equations. Ženeva: Indersci. Enterp. Ltd., 2011, roč. 3, 1-2, s. 84-131. ISSN 1752-3583.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. First order conditions for generalized variational problems over time scales. Computers & Mathematics with Applications. Elsevier Science Ltd., 2011, roč. 62, č. 9, s. 3490-3503. ISSN 0898-1221. Dostupné z: https://doi.org/10.1016/j.camwa.2011.08.065.

ŠIMON HILSCHER, Roman. On general Sturmian theory for abnormal linear Hamiltonian systems. In W. Feng, Z. Feng, M. Grasselli, A. Ibragimov, X. Lu, S. Siegmund, J. Voigt. Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Springfield, Missouri: AIMS (American Institute of Mathematical Sciences), 2011, s. 684-691. ISBN 978-1-60133-007-9. Dostupné z: https://doi.org/10.3934/proc.2011.2011.684.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. Int. J. Difference Equ. Delhi: Research India Publications, 2011, roč. 6, č. 1, s. 39-51. ISSN 0973-6069.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Rayleigh principle for time scale symplectic systems and applications. Electronic Journal of Qualitative Theory of Differential Equations. Szeged, 2011, roč. 2011, č. 83, s. 1-26. ISSN 1417-3875.

ŠIMON HILSCHER, Roman. Sturmian theory for linear Hamiltonian systems without controllability. Mathematische Nachrichten. Berlín: Wiley Inter Science, 2011, roč. 284, č. 7, s. 831-843. ISSN 0025-584X.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Weyl-Titchmarsh theory for time scale symplectic systems on half line. Abstract and Applied Analysis. New York: Hindawi Publishing Corporation, 2011, roč. 2011, č. 738520, s. 1-41. ISSN 1085-3375. Dostupné z: https://doi.org/10.1155/2011/738520.

DOŠLÁ, Zuzana; Robert MAŘÍK; Roman ŠIMON HILSCHER a Jiří ŠREMR. Abstract Book of CDEIT 2010. 1. vyd. Brno: Masarykova univerzita, 2010, 122 s. ISBN 978-80-210-5289-5.

DOŠLÁ, Zuzana; Robert MAŘÍK; Roman ŠIMON HILSCHER; Jiří ŠREMR; Simona FIŠNAROVÁ; Milan TVRDÝ a Karel LEPKA. Colloquium on Differential Equations and Integration Theory. 2010.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Mathematica Bohemica. Praha: Matematický ústav AV ČR, 2010, roč. 315, č. 2, s. 209-222. ISSN 0862-7959.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Nabla time scale symplectic systems and related quadratic functionals. Differential Equations and Dynamical Systems. Springer India, 2010, roč. 18, 1-2, s. 163-198. ISSN 0971-3514.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Reid roundabout theorems for time scale symplectic systems. In Discrete Dynamics and Difference Equations. 1. vyd. Londýn: World Scientific Publishing Co., 2010, s. 267-288. ISBN 978-981-4287-64-7.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Symmetric three-term recurrence equations and their symplectic structure. Advances in Difference Equations. New York: Hindawi Publishing Corporation, 2010, roč. 2010, ID 626942, 17 s. ISSN 1687-1839.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Symplectic structure of Jacobi systems on time scales. International Journal of Difference Equations. Delhi (Indie): Research India Publications, 2010, roč. 5, č. 1, s. 55-81. ISSN 0973-6069.

ŠIMON HILSCHER, Roman. A note on the time scale calculus of variations problems. Ulm: University of Ulm, 2009, 8 s. Ulmer Seminare 14.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey. International Journal of Difference Equations. Delhi (Indie): Research India Publications, 2009, roč. 4, č. 1, s. 49-67. ISSN 0973-6069.

ŠIMON HILSCHER, Roman; Werner KRATZ a Vera Michel ZEIDAN. Differentiation of solutions of dynamic equations on time scales with respect to parameters. Advances in Dynamical Systems and Applications. Delhi (Indie): Research India Publications, 2009, roč. 4, č. 1, s. 35-54. ISSN 0973-5321.

ŠIMON HILSCHER, Roman. Eigenvalue, oscillation, and variational results for time scale symplectic systems. In International Conference on Differential Equations and Their Applications (Equadiff 12). 2009.

ŠIMON HILSCHER, Roman; Ondřej DOŠLÝ; Jan ČERMÁK; Josef DIBLÍK; Zuzana DOŠLÁ; Robert HAKL; Karel LEPKA; Alexander LOMTATIDZE; Pavel ŘEHÁK; Zdeněk ŠMARDA; Zdeněk SVOBODA a Simona FIŠNAROVÁ. International Conference on Differential Equations and Their Applications (Equadiff 12). 2009.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Multiplicities of focal points for discrete symplectic systems: revisited. Journal of Difference Equations and Applications. Taylor and Francis, 2009, roč. 15, č. 10, s. 1001-1010. ISSN 1023-6198.

ŠIMON HILSCHER, Roman a Vera ZEIDAN. Oscillation results for time scale symplectic systems. In Proceedings of the 14th International Conference on Difference Equations and Applications. Istanbul: Ugur-Bahcesehir University Publishing Company, 2009, s. 203-210. ISBN 978-975-6437-80-3.

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Picone type identities and definiteness of quadratic functionals on time scales. Applied Mathematics and Computation. Elsevier, 2009, roč. 215, č. 7, s. 2425–2437. ISSN 0096-3003.

ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Trigonometric and hyperbolic systems on time scales. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 2009, roč. 18, 3-4, s. 483-506. ISSN 1056-2176.

ŠIMON HILSCHER, Roman a Vera ZEIDAN. Weak maximum principle and accessory problem for control problems on time scales. Nonlinear Analysis. 2009, roč. 70, č. 9, s. 3209-3226. ISSN 0362-546X.

HILSCHER, Roman a Vera ZEIDAN. Applications of time scale symplectic systems without normality. Journal of Mathematical Analysis and Applications. San Diego (USA): Elsevier Science, 2008, roč. 340, č. 1, s. 451-465. ISSN 0022-247X.

HILSCHER, Roman a Vera Michel ZEIDAN. Riccati equations for abnormal time scale quadratic functionals. Journal of Differential Equations. San Diego (USA): Elsevier Science, 2008, roč. 244, č. 6, s. 1410-1447. ISSN 0022-0396.

HILSCHER, Roman a Christopher C. TISDELL. Terminal value problems for first and second order nonlinear equations on time scales. Electronic Journal of Differential Equations. San Marcos, TX 78666, USA: Texas State University - San Marcos, 2008, roč. 2008, č. 68, s. 1-21. ISSN 1072-6691.

HILSCHER, Roman a Vera ZEIDAN. Time scale embedding theorem and coercivity of quadratic functionals. Analysis (Munich). Mnichov: Oldenbourg Wissenschaftsverlag, 2008, roč. 28, č. 1, s. 1-28. ISSN 0174-4747.

HILSCHER, Roman a Vera ZEIDAN. Extension of discrete LQR-problem to symplectic systems. International Journal of Difference Equations. Delhi (Indie): Research India Publications, 2007, roč. 2, č. 2, s. 197-208. ISSN 0973-6069.

HILSCHER, Roman a Vera ZEIDAN. Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 2007, roč. 16, č. 3, s. 451-480. ISSN 1056-2176.

HILSCHER, Roman a Viera RŮŽIČKOVÁ. Perturbation of nonnegative time scale quadratic functionals. In Difference Equations, Special Functions, and Orthogonal Polynomials. Londýn: World Scientific, 2007, s. 266-275. ISBN 978-981-270-643-0.

HILSCHER, Roman a Viera RŮŽIČKOVÁ. Perturbation of time scale quadratic functionals with variable endpoints. Advances in Dynamical Systems and Applications. Delhi (Indie): Research India Publications, 2007, roč. 2, č. 2, s. 207-224. ISSN 0973-5321.

ŠIMON HILSCHER, Roman. Přednášky MB102 Matematika II. Brno: Fakulta informatiky, Masarykova univerzita, 2007, 144 s.

DOŠLÝ, Ondřej; Zuzana DOŠLÁ; Pavel ŘEHÁK; Roman HILSCHER; Miroslav BARTUŠEK; Zdeněk POSPÍŠIL a Štefan SCHWABIK. Colloquium on Differential and Difference Equations. 2006.

HILSCHER, Roman. Comparison results for solutions of time scale matrix Riccati equations and inequalities. The Australian Journal of Mathematical Analysis and Applications. Victoria, Austrálie: Australian Internet Publishing, 2006, roč. 3, č. 2, s. Article 13, 1-15, 15 s. ISSN 1449-5910.

HILSCHER, Roman a Vera ZEIDAN. Coupled intervals for discrete symplectic systems. Linear Algebra and its Applications. USA: Elsevier Science, 2006, roč. 419, 2-3, s. 750-764. ISSN 0024-3795.

HILSCHER, Roman a Viera RŮŽIČKOVÁ. Implicit Riccati equations and quadratic functionals for discrete symplectic systems. International Journal of Difference Equations. Delhi (Indie): Research India Publications, 2006, roč. 1, č. 1, s. 135-154. ISSN 0973-6069.

ŠIMON HILSCHER, Roman. Přednášky MB101 Matematika I. Brno: Fakulta informatiky, Masarykova univerzita, 2006, 157 s.

HILSCHER, Roman a Viera RŮŽIČKOVÁ. Riccati inequality and other results for discrete symplectic systems. Journal of Mathematical Analysis and Applications. San Diego (USA): Elsevier Science, 2006, roč. 322, č. 2, s. 1083-1098. ISSN 0022-247X.

HILSCHER, Roman a Vera ZEIDAN. Time scale symplectic systems without normality. Journal of Differential Equations. San Diego (USA): Elsevier Science, 2006, roč. 230, č. 1, s. 140-173. ISSN 0022-0396.

BOHNER, Martin a Roman HILSCHER. An eigenvalue problem for linear Hamiltonian dynamic systems. Fasciculi Mathermatici. Poznaň, Polsko: Politechnika Poznaňska, Institut Mat., 2005, roč. 35, č. 1, s. 35-49. ISSN 0044-4413.

HILSCHER, Roman a Vera ZEIDAN. Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey. Journal of Difference Equations and Applications. Taylor and Francis, 2005, roč. 11, č. 9, s. 857-875. ISSN 1023-6198.

HILSCHER, Roman a Vera ZEIDAN. Solvability of the discrete LQR-problem under minimal assumptions. In Difference Equations and Discrete Dynamical Systems. London: World Scientific Publishing Co., 2005, s. 273-282. ISBN 981-256-520-5.

HILSCHER, Roman a Vera ZEIDAN. Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints. Journal of Mathematical Analysis and Applications. San Diego (USA): Elsevier Science, 2004, roč. 289, č. 1, s. 143-166. ISSN 0022-247X.

HILSCHER, Roman a Vera ZEIDAN. Coupled intervals in the discrete optimal control. Journal of Difference Equations and Applications. Taylor and Francis, 2004, roč. 10, č. 2, s. 151-186. ISSN 1023-6198.

HILSCHER, Roman a Vera ZEIDAN. Discrete quadratic functionals with jointly varying endpoints via separable endpoints. In Proceedings of the Sixth International Conference on Difference Equations. Boca Raton: Chapman & Hall/CRC, 2004, s. 461-470. ISBN 0-415-31675-8.

HILSCHER, Roman a Vera ZEIDAN. Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Mathematische Nachrichten. Berlin: WILEY-VCH Verlag, 2004, roč. 266, č. 1, s. 48-59. ISSN 0025-584X.

DOŠLÝ, Ondřej a Roman HILSCHER. A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD. Comput Math. Appl. 2003, roč. 45, č. 1, s. 961-981. ISSN 0898-1221.

HILSCHER, Roman a Vera ZEIDAN. A remark on discrete quadratic functionals with separable endpoints. Rocky Mountain Journal of Mathematics. 2003, roč. 33, č. 4, s. 1337-1351. ISSN 0035-7596.

BOHNER, Martin; Ondřej DOŠLÝ; Roman HILSCHER a Werner KRATZ. Diagonalization approach to discrete quadratic functionals. Archives of Inequalities and Applications. Atlanta, Georgia, USA: Dynamic Publishers, Inc., 2003, roč. 1, č. 2, s. 261-274. ISSN 1542-6149.

HILSCHER, Roman a Vera ZEIDAN. Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Computers & mathematics with applications. New York: Pergamon Press, 2003, roč. 45, 6-9, s. 1369-1383. ISSN 0097-4943.

DOŠLÝ, Ondřej; Roman HILSCHER a Vera ZEIDAN. Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Linear Algebra and its Applications. USA: Elsevier Science, 2003, roč. 375, 1.12.2003, s. 21-44. ISSN 0024-3795.

HILSCHER, Roman a Pavel ŘEHÁK. Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 2003, roč. 12, 1-2, s. 171-189. ISSN 1056-2176.

HILSCHER, Roman a Vera ZEIDAN. Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals. Linear Algebra and its Applications. USA: Elsevier Science, 2003, roč. 367, č. 1, s. 67-104. ISSN 0024-3795.

DOŠLÝ, Ondřej; Stefan HILGER a Roman HILSCHER. Symplectic dynamic systems. In Advances in Dynamic Equations on Time Scales, M. Bohner and A. Peterson, editors. Boston: Birkhauser, 2003, s. 345-392. Normální knížka. ISBN 0-8176-4293-5.

HILSCHER, Roman. A time scales version of a Wirtinger type inequality and applications. Journal of Computational and Applied Mathematics. Elsevier Science, 2002, roč. 141, 1-2, s. 219-226. ISSN 0377-0427.

HILSCHER, Roman a Vera ZEIDAN. Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Journal of Mathematical Analysis and Applications. USA: Acad.Press, 2002, roč. 276, č. 1, s. 396-421. ISSN 0022-247X.

HILSCHER, Roman a Vera ZEIDAN. Discrete optimal control: second order optimality conditions. Journal of Difference Equations and Applications. Taylor and Francis, 2002, roč. 8, č. 10, s. 875-896. ISSN 1023-6198.

HILSCHER, Roman a Vera ZEIDAN. Second order sufficiency criteria for a discrete optimal control problem. Journal of Difference Equations and Applications. Taylor and Francis, 2002, roč. 8, č. 6, s. 573-602. ISSN 1023-6198.

DOŠLÝ, Ondřej a Roman HILSCHER. Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. J. Difference Equations Appl. San Diego, 2001, roč. 7, č. 3, s. 265-294. ISSN 1023-6198.

HILSCHER, Roman. Discrete spectra criteria for certain classes of singular diffferential and difference operators. Computers & mathematics with applications. New York: Pergamon Press, 2001, roč. 42, 3-5, s. 465-476. ISSN 0097-4943.

HILSCHER, Roman. Inhomogeneous quadratic functionals on time scales. Journal of Mathematical Analysis and Applications. USA: Acad.Press, 2001, roč. 253, č. 2, s. 473-481, 8 s. ISSN 0022-247X.

DOŠLÝ, Ondřej; Martin BOHNER a Roman HILSCHER. Linear Hamiltonian dynamic systems on time scales: Sturmian property of principal solution. Nonlin. Anal. Atlanta, 2001, roč. 47, č. 2, s. 849-859. ISSN 0362-546X.

HILSCHER, Roman. Positivity of quadratic functionals on time scales: necessity. Mathematische Nachrichten. Berlin: WILEY-VCH Verlag, 2001, roč. 226, č. 1, s. 85-98. ISSN 0025-584X.

HILSCHER, Roman. Reid roundabout theorem for symplectic dynamic systems on time scales. Applied Mathematics and Optimization. New York: Springer-Verlag, 2001, roč. 43, č. 2, s. 129-146. ISSN 0095-4616.

HILSCHER, Roman a Vera ZEIDAN. Discrete optimal control: the accessory problem and necessary optimality conditions. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press, 2000, roč. 243, č. 2, s. 429-452. ISSN 0022-247X.

HILSCHER, Roman. Linear Hamiltonian systems on time scales: positivity of quadratic functionals. Mathematical and Computer Modelling. Elsevier Science, 2000, roč. 32, 5-6, s. 507-527, 20 s. ISSN 0895-7177.

HILSCHER, Roman. On disconjugacy for vector linear Hamiltonian systems on time scales. In Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations. Amsterdam: Gordon and Breach, 2000, s. 181-188. ISBN 90-5699-688-6.

HILSCHER, Roman. Spectral properties of general self-adjoint, even order differential operators. Mathematica Slovaca. Bratislava: Slovak Academy of Sciences, 2000, roč. 50, č. 2, s. 165-186, 21 s. ISSN 0139-9918.

HILSCHER, Roman. Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Rocky Mountain Journal of Mathematics. 1999, roč. 29, č. 4, s. 1301-1319, 18 s. ISSN 0035-7596.

DOŠLÝ, Ondřej a Roman HILSCHER. Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Dyn. Syst. Appl. 1999, roč. 8, č. 2, s. 401-420. ISSN 1056-2176.

HILSCHER, Roman. Linear Hamiltonian systems on time scales: transformations. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 1999, roč. 8, 3-4, s. 489-501, 12 s. ISSN 1056-2176.

DOŠLÝ, Ondřej a Roman HILSCHER. Spectral properties of fourth order differential operators. Mathematica Bohemica : časopis pro pěstování matematiky. Praha: Matematický ústav AV ČR, 1997, roč. 122, č. 3, s. 153-168. ISSN 0862-7959.