Geodesic
The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities
Sbornik. Mathematics, Tome 206 (2015) no. 9, pp. 1281-1298

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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, discontinuous nonlinearity, semiregular solutions, the method of upper and lower solutions.
Mots-clés : equations of elliptic type 
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V. N. Pavlenko; D. K. Potapov. The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities. Sbornik. Mathematics, Tome 206 (2015) no. 9, pp. 1281-1298. http://geodesic.mathdoc.fr/item/SM_2015_206_9_a3/