Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains
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Date
2006
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GAUTHIER-VILLARS/EDITIONS ELSEVIER
Abstract
We consider the problem Delta u + \u\(4/n-2) u = 0 in Omega(epsilon), u = 0 on partial derivative Omega(epsilon), where Omega(epsilon) := Omega \ B (0, epsilon) and Omega is a bounded smooth domain in R(N), which contains the origin and is symmetric with respect to the origin, N >= 3 and epsilon is a positive parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up at the origin. (C) 2006 Elsevier Masson SAS. All rights reserved.
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Keywords
critical Sobolev exponent, sign changing solution, multiple blow up, BREZIS-NIRENBERG PROBLEM, MINIMAL NODAL SOLUTIONS, VARIATIONAL PROBLEM, SYMMETRIC DOMAIN, CRITICAL GROWTH, EQUATIONS, TOPOLOGY, HOLES, COMPACTNESS, EXISTENCE