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Sbornik: Mathematics, 2015, Volume 206, Issue 9, Pages 1281–1298
DOI: https://doi.org/10.1070/SM2015v206n09ABEH004496 (Mi sm8427) 		 
This article is cited in 12 scientific papers (total in 13 papers)

The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University
English version PDF (530 kB) Citations (13)
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DOI: https://doi.org/10.1070/SM2015v206n09ABEH004496
Abstract: This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions.
Bibliography: 32 titles.
Keywords: spectral problems, equations of elliptic type, discontinuous nonlinearity, semiregular solutions, the method of upper and lower solutions.
Received: 01.10.2014 and 06.01.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 9, Pages 121–138
DOI: https://doi.org/10.4213/sm8427
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35J25, 35J60, 35P30
Language: English
Original paper language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities”, Mat. Sb., 206:9 (2015), 121–138; Sb. Math., 206:9 (2015), 1281–1298
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:82
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