Rayleigh principle for linear Hamiltonian systems without controllability
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00057185" target="_blank" >RIV/00216224:14310/12:00057185 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1051/cocv/2011104" target="_blank" >http://dx.doi.org/10.1051/cocv/2011104</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/cocv/2011104" target="_blank" >10.1051/cocv/2011104</a>
Alternative languages
Result language
angličtina
Original language name
Rayleigh principle for linear Hamiltonian systems without controllability
Original language description
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools are the extended Picone formula, which is proven here for this general setting, results on piecewise constant kernels for conjoined bases of the Hamiltonian system, and the oscillation theorem relating the number of proper focal points of conjoined bases with the number of finite eigenvalues. As applicationswe obtain the expansion theorem in the space of admissible functions without controllability and a result on coercivity of the corresponding quadratic functional.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GC201%2F09%2FJ009" target="_blank" >GC201/09/J009: Oscillation and spectral theory of differential and difference systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ESAIM: Control, Optimisation and Calculus of Variations
ISSN
1292-8119
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
501-519
UT code for WoS article
000306431900010
EID of the result in the Scopus database
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