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

Journal Article · Wed Sep 30 00:00:00 EDT 2015 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2015V206N09ABEH004496· OSTI ID:22590450

Pavlenko, V N ^[1]; Potapov, D K ^[2]

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1. Chelyabinsk State University, Chelyabinsk (Russian Federation)
2. Saint Petersburg State University, St. Petersburg (Russian Federation)

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.

• OSTI ID: 22590450
• Journal Information: Sbornik. Mathematics, Vol. 206, Issue 9; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
DIRICHLET PROBLEM
EQUATIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS