Singular limits for the bi-Laplacian operator with exponential nonlinearity in R-4
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Date
2008
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Journal ISSN
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Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
Abstract
Let Omega be a bounded smooth domain in R-4 such that for some integer d >= 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem
{Delta(2)u - rho(4)k(x)e(u) = 0 in Omega,
u = Delta u = 0 on partial derivative Omega,
has a solution blowing-up, as rho -> 0, at m points of Omega, for any given number in. (C) 2007 Elsevier Masson SAS. All rights reserved.
{Delta(2)u - rho(4)k(x)e(u) = 0 in Omega,
u = Delta u = 0 on partial derivative Omega,
has a solution blowing-up, as rho -> 0, at m points of Omega, for any given number in. (C) 2007 Elsevier Masson SAS. All rights reserved.
Description
Keywords
CRITICAL SOBOLEV EXPONENT, LIOUVILLE-TYPE EQUATIONS, MEAN-FIELD EQUATION, ELLIPTIC EQUATION, UP SOLUTIONS, BLOW, QUANTIZATION, COMPACTNESS, EXISTENCE, PRINCIPLE