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@article{1109331,
author = {Šimon Hilscher, Roman},
article_number = {5-6},
doi = {http://dx.doi.org/10.1002/mana.201200314},
keywords = {Linear Hamiltonian system; Comparison of eigenvalues; Finite eigenvalue; Sturmian comparison theorem; Controllability; Strict normality; Self-adjoint eigenvalue problem; Oscillation theorem},
language = {eng},
issn = {0025-584X},
journal = {Mathematische Nachrichten},
title = {Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems},
volume = {287},
year = {2014}
}
TY - JOUR
ID - 1109331
AU - Šimon Hilscher, Roman
PY - 2014
TI - Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems
JF - Mathematische Nachrichten
VL - 287
IS - 5-6
SP - 704-716
EP - 704-716
PB - Wiley Inter Science
SN - 0025584X
KW - Linear Hamiltonian system
KW - Comparison of eigenvalues
KW - Finite eigenvalue
KW - Sturmian comparison theorem
KW - Controllability
KW - Strict normality
KW - Self-adjoint eigenvalue problem
KW - Oscillation theorem
N2 - In this work we derive new comparison results for (finite) eigenvalues of two self-adjoint linear Hamiltonian eigenvalue problems. The coefficient matrices depend on the spectral parameter nonlinearly and the spectral parameter is present also in the boundary conditions. We do not impose any controllability or strict normality assumptions. Our method is based on a generalization of the Sturmian comparison theorem for such systems. The results are new even for the Dirichlet boundary conditions, for linear Hamiltonian systems depending linearly on the spectral parameter, and for Sturm-Liouville eigenvalue problems with nonlinear dependence on the spectral parameter.
ER -
ŠIMON HILSCHER, Roman. Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. \textit{Mathematische Nachrichten}. Wiley Inter Science, 2014, roč.~287, 5-6, s.~704-716. ISSN~0025-584X. doi:10.1002/mana.201200314.
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