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A singularly perturbed elliptic problem involving supercritical Sobolev exponent*
Published online by Cambridge University Press: 14 November 2011
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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