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Matematicheskie Zametki, 2021, Volume 110, Issue 2, Pages 239–257
DOI: https://doi.org/10.4213/mzm12596
(Mi mzm12596)
 

This article is cited in 3 scientific papers (total in 3 papers)

Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University
Full-text PDF (561 kB) Citations (3)
References:
Abstract: For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.
Keywords: elliptic system, discontinuous nonlinearity, semiregular solution, upper solution, lower solution.
Received: 15.10.2019
Revised: 19.03.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 2, Pages 226–241
DOI: https://doi.org/10.1134/S0001434621070245
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
Language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities”, Mat. Zametki, 110:2 (2021), 239–257; Math. Notes, 110:2 (2021), 226–241
Citation in format AMSBIB
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\paper Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities
\jour Mat. Zametki
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\issue 2
\pages 239--257
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  • https://www.mathnet.ru/eng/mzm12596
  • https://doi.org/10.4213/mzm12596
  • https://www.mathnet.ru/eng/mzm/v110/i2/p239
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:36
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