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Sbornik: Mathematics, 2017, Volume 208, Issue 1, Pages 157–172
DOI: https://doi.org/10.1070/SM8562
(Mi sm8562)
 

This article is cited in 7 scientific papers (total in 8 papers)

Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University
References:
Abstract: The question on the existence of solutions to eigenvalue problems is treated for nonlinear equations with discontinuous operators in a real Hilbert space. Using a variational method, theorems on the existence of two nontrivial solutions for sufficiently large values of the spectral parameter are proved. As an application, eigenvalue problems for elliptic-type equations with nonlinear terms which are discontinuous in the phase variable are investigated.
Bibliography: 22 titles.
Keywords: eigenvalue problems, discontinuous right-hand side, variational method, nontrivial solution.
Received: 24.06.2015 and 31.03.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 1, Pages 165–182
DOI: https://doi.org/10.4213/sm8562
Bibliographic databases:
UDC: 517.98+517.95
MSC: Primary 35R05, 47J05; Secondary 49J40
Language: English
Original paper language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides”, Mat. Sb., 208:1 (2017), 165–182; Sb. Math., 208:1 (2017), 157–172
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM8562
  • https://www.mathnet.ru/eng/sm/v208/i1/p165
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:552
    Russian version PDF:50
    English version PDF:6
    References:72
    First page:36
     
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