Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains
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Date
2010
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TAYLOR & FRANCIS INC
Abstract
We consider the problem [image omitted] in epsilon, u=0 on epsilon, where epsilon: =\{B(a, epsilon) B(b, epsilon)}, with a bounded smooth domain in N, N epsilon 3, ab two points in , and epsilon is a positive small parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up both at a and at b.
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Keywords
Blowing-up solution, Critical Sobolev exponent, Robin's function, Tower of bubbles, CRITICAL SOBOLEV EXPONENT, BAHRI-CORON PROBLEM, BREZIS-NIRENBERG PROBLEM, MINIMAL NODAL SOLUTIONS, CRITICAL GROWTH, VARIATIONAL PROBLEM, SYMMETRIC DOMAIN, R-N, EQUATIONS, EXISTENCE