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Sbornik: Mathematics, 2017, Volume 208, Issue 6, Pages 842–862
DOI: https://doi.org/10.1070/SM8587 (Mi sm8587) 		 
Boundary value problems for a nonlinear elliptic equation

Yu. V. Egorov

Institute de Mathématique de Toulouse, Université Paul Sabatier, France
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DOI: https://doi.org/10.1070/SM8587
Abstract: It is proved that the Dirichlet and Neumann problems for a nonlinear second-order elliptic equation have infinitely many solutions. The spectrum of these problems is studied and the weak convergence of the normed eigenfunctions to zero is established.
Bibliography: 10 titles.
Keywords: nonlinear elliptic equation, Dirichlet problem, Neumann problem, eigenfunctions.
Received: 24.08.2015 and 15.04.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 6, Pages 109–129
DOI: https://doi.org/10.4213/sm8587
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: Primary 47H15; Secondary 58E05
Language: English
Original paper language: Russian
Citation: Yu. V. Egorov, “Boundary value problems for a nonlinear elliptic equation”, Mat. Sb., 208:6 (2017), 109–129; Sb. Math., 208:6 (2017), 842–862
Citation in format AMSBIB
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    Abstract page:512
    Russian version PDF:50
    English version PDF:12
    References:51
    First page:37
     
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