About: Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter

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About: Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in 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 the eigenvalue problem for the second order Sturm-Liouville differential equation and the Dirichlet boundary conditions. Our setting is more general than in the current literature in two respects: (i) the coefficients depend on the spectral parameter lambda in general nonlinearly, and (ii) the potential is merely monotone in lambda and not necessarily strictly monotone in lambda, so that the usual strict normality assumption is now removed. This general setting leads to new definitions of an eigenvalue and an eigenfunction - called a finite eigenvalue and a finite eigenfunction. With these new concepts we show that the finite eigenvalues are isolated, bounded from below, and establish an oscillation theorem, i.e., a result counting the zeros of the finite eigenfunctions. The traditional theory in which the potential is linear and strictly monotone in lambda nicely follows from our results. In this paper, we consider the eigenvalue problem for the second order Sturm-Liouville differential equation and the Dirichlet boundary conditions. Our setting is more general than in the current literature in two respects: (i) the coefficients depend on the spectral parameter lambda in general nonlinearly, and (ii) the potential is merely monotone in lambda and not necessarily strictly monotone in lambda, so that the usual strict normality assumption is now removed. This general setting leads to new definitions of an eigenvalue and an eigenfunction - called a finite eigenvalue and a finite eigenfunction. With these new concepts we show that the finite eigenvalues are isolated, bounded from below, and establish an oscillation theorem, i.e., a result counting the zeros of the finite eigenfunctions. The traditional theory in which the potential is linear and strictly monotone in lambda nicely follows from our results. (en)
Title	Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter (en)
skos:prefLabel	Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter (en)
skos:notation	RIV/00216224:14310/13:00066009!RIV14-MSM-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
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	94681
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/13:00066009
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Sturm-Liouville differential equation; nonlinear dependence on spectral parameter; finite eigenvalue; finite eigenfunction; oscillation theorem (en)
http://linked.open.../riv/klicoveSlovo	Sturm-Liouville differential equation finite eigenfunction finite eigenvalue nonlinear dependence on spectral parameter oscillation theorem
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[97308B5E1887]
http://linked.open...i/riv/nazevZdroje	Dynamic Systems and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	22
http://linked.open...iv/tvurceVysledku	Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000328805600008
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	1056-2176
number of pages	10 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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