On a Nonclassical Eigenvalue Problem with Nonlinearizable Solutions

We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary conditions of the first kind and two additional local conditions. There is one spectral parameter in the problem, and two more parameters, which are...

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Published inDifferential equations Vol. 59; no. 3; pp. 301 - 311
Main Authors Valovik, D. V., Martynova, V. Yu
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2023
Springer
Springer Nature B.V
Subjects
Boundary conditions
Difference and Functional Equations
Differential equations
Eigenvalues
Electrodynamics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Parameters
Partial Differential Equations
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Summary:We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary conditions of the first kind and two additional local conditions. There is one spectral parameter in the problem, and two more parameters, which are subject to an additional constraint, occur in the above-mentioned local conditions. Thus, there are two unknown parameters in the problem: one is the spectral parameter, and the other is some additional parameter, chosen so as to ensure that there exists a nontrivial solution of the problem in question. The existence of nonlinearizable solutions of the problem is proved.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123030023