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Type: Artigo de periódico
Title: Concentration for an elliptic equation with singular nonlinearity
Author: Davila, J
Montenegro, M
Abstract: We are interested in nontrivial solutions of the equation: -Delta u + chi(-beta)(vertical bar u > 0 vertical bar u) = lambda u(p), u >= 0 in Omega, with u = 0 on partial derivative Omega. where Omega subset of R-N, N >= 2, is a bounded domain with smooth boundary, 0 < beta < 1, 1 <= p < N+2/N-2 if N >= 3 (p >= 1 if N = 2) and lambda > 0. If p > 1 we prove existence of nontrivial solutions for every lambda > 0. As lambda -> +infinity we find that the least energy solutions concentrate around a point that maximizes the distance to the boundary. We also study the behavior as lambda -> 0. When p = 1 we have similar results, extending previous works for radial solutions in a ball. (C) 2011 Elsevier Masson SAS. All rights reserved.
Subject: Elliptic equations
Singular nonlinearity
Asymptotic behavior
Country: França
Editor: Gauthier-villars/editions Elsevier
Rights: fechado
Identifier DOI: 10.1016/j.matpur.2011.02.001
Date Issue: 2012
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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