ŠEPITKA, Peter and 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, vol. 266, No 11, p. 7481-7524. ISSN 0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2018.12.007. |
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@article{1475127, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_location = {San Diego}, article_number = {11}, doi = {http://dx.doi.org/10.1016/j.jde.2018.12.007}, keywords = {Linear Hamiltonian system; Proper focal point; Principal solution; Antiprincipal solution; Controllability}, language = {eng}, issn = {0022-0396}, journal = {Journal of Differential Equations}, title = {Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems}, url = {https://www.sciencedirect.com/science/article/pii/S0022039618306958}, volume = {266}, year = {2019} }
TY - JOUR ID - 1475127 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2019 TI - Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems JF - Journal of Differential Equations VL - 266 IS - 11 SP - 7481-7524 EP - 7481-7524 PB - ACADEMIC PRESS INC ELSEVIER SCIENCE SN - 00220396 KW - Linear Hamiltonian system KW - Proper focal point KW - Principal solution KW - Antiprincipal solution KW - Controllability UR - https://www.sciencedirect.com/science/article/pii/S0022039618306958 L2 - https://www.sciencedirect.com/science/article/pii/S0022039618306958 N2 - In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case. ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. \textit{Journal of Differential Equations}. San Diego: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2019, vol.~266, No~11, p.~7481-7524. ISSN~0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2018.12.007.
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