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@article{968899,
author = {Šimon Hilscher, Roman and Zeidan, Vera Michel},
article_location = {Spojené státy americké},
article_number = {17},
doi = {http://dx.doi.org/10.1016/j.amc.2012.01.056},
keywords = {Oscillation theorem; Rayleigh principle; Linear Hamiltonian system; Time scale symplectic system; Discrete symplectic system; Finite eigenvalue; Finite eigenfunction; Quadratic functional; Positivity; Selfadjoint eigenvalue problem},
language = {eng},
issn = {0096-3003},
journal = {Applied Mathematics and Computation},
title = {Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions},
volume = {218},
year = {2012}
}
TY - JOUR
ID - 968899
AU - Šimon Hilscher, Roman - Zeidan, Vera Michel
PY - 2012
TI - Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions
JF - Applied Mathematics and Computation
VL - 218
IS - 17
SP - 8309-8328
EP - 8309-8328
PB - Elsevier
SN - 00963003
KW - Oscillation theorem
KW - Rayleigh principle
KW - Linear Hamiltonian system
KW - Time scale symplectic system
KW - Discrete symplectic system
KW - Finite eigenvalue
KW - Finite eigenfunction
KW - Quadratic functional
KW - Positivity
KW - Selfadjoint eigenvalue problem
N2 - The aim of this paper is to establish the oscillation theorems, Rayleigh principle, and coercivity results for linear Hamiltonian and symplectic systems with general boundary conditions, i.e., for the case of separated and jointly varying endpoints, and with no controllability (normality) and strong observability assumptions. Our method is to consider the time interval as a time scale and apply suitable time scales techniques to reduce the problem with separated endpoints into a problem with Dirichlet boundary conditions, and the problem with jointly varying endpoints into a problem with separated endpoints. These more general results on time scales then provide new results for the continuous time linear Hamiltonian systems as well as for the discrete symplectic systems. This paper also solves an open problem of deriving the oscillation theorem for problems with periodic boundary conditions. Furthermore, the present work demonstrates the utility and power of the analysis on time scales in obtaining new results especially in the classical continuous and discrete time theories.
ER -
ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. \textit{Applied Mathematics and Computation}. Spojené státy americké: Elsevier, 2012, roč.~218, č.~17, s.~8309-8328. ISSN~0096-3003. doi:10.1016/j.amc.2012.01.056.
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