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A singularly perturbed elliptic problem involving supercritical Sobolev exponent*

Published online by Cambridge University Press:  14 November 2011

Yaotian Shen  and
Shusen Yan
Yaotian Shen
Affiliation:
Department of Applied Mathematics, South China University of Technology, Guangzhou, P.R. China
Shusen Yan
Affiliation:
Department of Applied Mathematics, South China University of Technology, Guangzhou, P.R. China
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Abstract

This paper deals with −Δu + εuq−1 = u2*−1, , where q > 2*, ε > 0. We first show that the minimiser of the associated minimisation problem blows up at the global minimum point of H(x, x), where H(y, x) is the regular part of the Green's function. We then prove that for each strictly local minimum point x0 of H(x, x), this problem has a solution concentrating at x0 as ε→0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 809 - 819
Copyright
Copyright © Royal Society of Edinburgh 1998

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