ŠEPITKA, Peter and 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, vol. 487, No 2, p. 1-14. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2020.124030. |
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@article{1634316, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_location = {San Diego}, article_number = {2}, doi = {http://dx.doi.org/10.1016/j.jmaa.2020.124030}, keywords = {Sturmian comparison theorem; linear Hamiltonian system; Focal point; Complete controllability; principal solution; Sturm-Liouville equation}, language = {eng}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, title = {Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case}, url = {http://dx.doi.org/10.1016/j.jmaa.2020.124030}, volume = {487}, year = {2020} }
TY - JOUR ID - 1634316 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2020 TI - Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case JF - Journal of Mathematical Analysis and Applications VL - 487 IS - 2 SP - 1-14 EP - 1-14 PB - Elsevier SN - 0022247X KW - Sturmian comparison theorem KW - linear Hamiltonian system KW - Focal point KW - Complete controllability KW - principal solution KW - Sturm-Liouville equation UR - http://dx.doi.org/10.1016/j.jmaa.2020.124030 L2 - http://dx.doi.org/10.1016/j.jmaa.2020.124030 N2 - In this paper we consider two linear Hamiltonian differential systems on an open unbounded interval. We assume that the systems are completely controllable and satisfy the Sturmian majorant condition and the Legendre condition. We derive a singular Sturmian comparison theorem for the case when the minorant system has a solution, which is principal at both endpoints of the considered interval. The main result is new even for the second order differential equations and it generalizes the singular comparison theorem obtained by Aharonov and Elias (2010). We illustrate our new theory by several examples. ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. \textit{Journal of Mathematical Analysis and Applications}. San Diego: Elsevier, 2020, vol.~487, No~2, p.~1-14. ISSN~0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2020.124030.
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