Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity

DOI10.1016/j.jde.2016.01.004zbMath1338.34036OpenAlexW2281186081MaRDI QIDQ5963855

Roman Šimon Hilscher, Peter Šepitka

Publication date: 26 February 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.01.004

zbMATH Keywords

controllabilitylinear Hamiltonian systemantiprincipal solution at infinitygenus of conjoined basesprincipal solution at infinityRiccati differential equation

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Comparative index and Sturmian theory for linear Hamiltonian systems ⋮ Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases ⋮ Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications ⋮ Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties ⋮ On the solvability of the Yakubovich linear-quadratic infinite horizon minimization problem ⋮ Focal points and principal solutions of linear Hamiltonian systems revisited ⋮ Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems ⋮ Riccati equations for linear Hamiltonian systems without controllability condition ⋮ On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems ⋮ Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval ⋮ Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems ⋮ Genera of conjoined bases for (non)oscillatory linear Hamiltonian systems: extended theory

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