Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00066009" target="_blank" >RIV/00216224:14310/13:00066009 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter
Original language 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 onthe 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.
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/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</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
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Dynamic Systems and Applications
ISSN
1056-2176
e-ISSN
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Volume of the periodical
22
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
115-124
UT code for WoS article
000328805600008
EID of the result in the Scopus database
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