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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm8562https://doi.org/10.1070/SM8562 https://www.mathnet.ru/eng/sm/v208/i1/p165
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Abstract page: | 552 | Russian version PDF: | 50 | English version PDF: | 6 | References: | 72 | First page: | 36 |
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