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Type: Artigo de periódico
Title: Existence of Solutions to a Singular Elliptic Equation
Author: Montenegro, M
Abstract: We study the equation -Delta u = (-1/u(beta) +lambda u(p))chi{u>0} in Omega with Dirichlet boundary condition, where 0 < p < 1 and 0 < beta < 1. We regularize the term 1/u(beta) near u similar to 0 by using a function g(epsilon)(u) which pointwisely tends to 1/u(beta) as epsilon -> 0. When the parameter lambda > 0 is large enough, the corresponding energy functional has critical points u(epsilon). Letting epsilon -> 0, then u(epsilon) converges to a solution of the original problem, which is nontrivial, nonnegative and vanishes at some portion of Omega. There are two nontrivial solutions.
Subject: Singular problems
multiple solutions
variational methods
Country: Suíça
Editor: Birkhauser Verlag Ag
Citation: Milan Journal Of Mathematics. Birkhauser Verlag Ag, v. 79, n. 1, n. 293, n. 301, 2011.
Rights: fechado
Identifier DOI: 10.1007/s00032-011-0152-9
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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