Boundary value problems for a nonlinear elliptic equation

Yu. V. Egorov

Institute de Mathématique de Toulouse, Université Paul Sabatier, France

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.

UDC: 517.957

MSC: Primary 47H15; Secondary 58E05

Received: 24.08.2015 and 15.04.2016

DOI: 10.4213/sm8587

 English version: Sbornik: Mathematics, 2017, 208:6, 842–862

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