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Type: Artigo de periódico
Title: Stable solutions for the bilaplacian with exponential nonlinearity
Author: Davila, J
Dupaigne, L
Guerra, I
Montenegro, M
Abstract: Let lambda* > 0 denote the largest possible value of lambda such that {Delta(2)u = lambda e(u) in B, u =partial derivative u/partial derivative n = 0 on partial derivative B} has a solution, where B is the unit ball in R-N and n is the exterior unit normal vector. We show that for lambda = lambda* this problem possesses a unique weak solution u*. We prove that u* is smooth if N <= 12 and singular when N >= 13, in which case u*( r) = - 4 log r + log( 8( N - 2)( N - 4)/lambda*) + o( 1) as r -> 0. We also consider the problem with general constant Dirichlet boundary conditions.
Subject: biharmonic
singular solutions
Country: EUA
Editor: Siam Publications
Rights: aberto
Identifier DOI: 10.1137/060665579
Date Issue: 2007
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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