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Mat. Zametki, 2017, Volume 101, Issue 2, Pages 247–261 (Mi mz10743)  

This article is cited in 1 scientific paper (total in 2 paper)

Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University

Abstract: We consider a strongly resonant homogeneous Dirichlet problem for elliptic-type equations with discontinuous nonlinearity in the phase variable. Using the variational method, we prove an existence theorem for at least three nontrivial solutions of the problem under consideration; at least two of these are semiregular. The resulting theorem is applied to the eigenvalue problem for elliptic-type equations with discontinuous nonlinearity with positive spectral parameter. An example of a discontinuous nonlinearity satisfying all the assumptions of the theorem is given.

Keywords: elliptic boundary-value problem, strong resonance, discontinuous nonlinearity, nontrivial and semiregular solution.

DOI: https://doi.org/10.4213/mzm10743

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English version:
Mathematical Notes, 2017, 101:2, 284–296

Bibliographic databases:

UDC: 517.95
Received: 16.02.2015
Revised: 24.06.2015

Citation: V. N. Pavlenko, D. K. Potapov, “Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance”, Mat. Zametki, 101:2 (2017), 247–261; Math. Notes, 101:2 (2017), 284–296

Citation in format AMSBIB
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\by V.~N.~Pavlenko, D.~K.~Potapov
\paper Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance
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\vol 101
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\pages 247--261
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  • https://doi.org/10.4213/mzm10743
  • http://mi.mathnet.ru/eng/mz/v101/i2/p247

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    This publication is cited in the following articles:
    1. S. M. Voronin, S. F. Dolbeeva, O. N. Dementev, A. A. Ershov, M. G. Lepchinskii, S. V. Matveev, N. B. Medvedeva, D. K. Potapov, E. A. Rozhdestvenskaya, E. A. Sbrodova, I. M. Sokolinskaya, A. A. Solovev, V. I. Ukhobotov, V. E. Fedorov, “K 70-letiyu professora Vyacheslava Nikolaevicha Pavlenko”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 383–387  mathnet  elib
    2. A. V. Arutyunov, S. E. Zhukovskii, “Variational Principles in Nonlinear Analysis and Their Generalization”, Math. Notes, 103:6 (2018), 1014–1019  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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