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Dal'nevost. Mat. Zh., 2012, Volume 12, Number 1, Pages 86–88 (Mi dvmg230)  

On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity

D. K. Potapov

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes

Abstract: We consider the question of existence of Dirichlets problem solution for the Laplace equation with a spectral parameter and discontinuous on a phase variable nonlinearity. Using the variational method, we prove a theorem about a number of solutions. We result an example of discontinuous nonlinearity that satisfies to conditions of the theorem for which there is unique semiregular solution of this boundary problem.

Key words: Dirichlets problem, the Laplace equation, spectral parameter, discontinuous nonlinearity, variational method, number of solutions.

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UDC: 517.95
MSC: Primary 35J25; Secondary 35J60
Received: 28.11.2011

Citation: D. K. Potapov, “On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity”, Dal'nevost. Mat. Zh., 12:1 (2012), 86–88

Citation in format AMSBIB
\Bibitem{Pot12}
\by D.~K.~Potapov
\paper On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
\jour Dal'nevost. Mat. Zh.
\yr 2012
\vol 12
\issue 1
\pages 86--88
\mathnet{http://mi.mathnet.ru/dvmg230}


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