About: Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

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About: Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of proper focal points of the principal solution of the system in the considered interval. We also define the corresponding geometric multiplicity of finite eigenvalues in terms of finite eigenfunctions and prove that the algebraic and geometric multiplicities coincide. In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of proper focal points of the principal solution of the system in the considered interval. We also define the corresponding geometric multiplicity of finite eigenvalues in terms of finite eigenfunctions and prove that the algebraic and geometric multiplicities coincide. (en)
Title	Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter (en)
skos:prefLabel	Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter (en)
skos:notation	RIV/00216224:14310/12:00057204!RIV13-GA0-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GC201/09/J009), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	11-12
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	157159
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/12:00057204
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Linear Hamiltonian system; Self-adjoint eigenvalue problem; Proper focal point; Conjoined basis; Finite eigenvalue; Oscillation; Controllability; Normality; Quadratic functional (en)
http://linked.open.../riv/klicoveSlovo	Self-adjoint eigenvalue problem Controllability Conjoined basis Finite eigenvalue Linear Hamiltonian system Normality Proper focal point Quadratic functional Oscillation
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[0E1D0F6FC7B7]
http://linked.open...i/riv/nazevZdroje	Mathematische Nachrichten
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Oscillation and spectral theory of differential and difference systems
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	285
http://linked.open...iv/tvurceVysledku	Kratz, Werner Šimon Hilscher, Roman Bohner, Martin
http://linked.open...ain/vavai/riv/wos	000307008700006
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	0025-584X
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1002/mana.201100172
http://localhost/t...ganizacniJednotka	14310

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