Multiparameter Eigenvalue Problems and Their Applications in Electrodynamics

A nonlinear n -parametric eigenvalue problem called the problem P is considered. In addition to n spectral parameters, the problem P depends on n 2 numerical parameters; for zero values of these parameters, the problem splits into n linear problems P i 0 , i = 1 , n ¯ . To the problem P , one can as...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 267; no. 6; pp. 677 - 697
Main Authors Valovik, D. V., Kurseeva, V. Yu
Format Journal Article
LanguageEnglish
Published New York Springer US 04.11.2022
Springer
Springer Nature B.V
Subjects
Eigenvalues
Electrodynamics
Mathematics
Mathematics and Statistics
Parameters
multiparameter eigenvalue problem
method of integral dispersion equations
nonlinear Sturm–Liouville-type problem
35P30
35Q61
perturbation method
47H14
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Summary:A nonlinear n -parametric eigenvalue problem called the problem P is considered. In addition to n spectral parameters, the problem P depends on n 2 numerical parameters; for zero values of these parameters, the problem splits into n linear problems P i 0 , i = 1 , n ¯ . To the problem P , one can assign n nonlinear problems P i , which, in particular, have solutions that are not related to the solutions of the problems P i 0 . The problems P i are treated in this work as “nonperturbed” problems. Using the properties of eigenvalues of the problems P i , we prove the existence of eigenvalues of the problem P ; some of these eigenvalues are not related to solutions of the problems P i 0 .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06173-4