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Non-degeneracy of least-energy solutions for an elliptic problem with nearly critical nonlinearity

Published online by Cambridge University Press:  04 February 2010

Futoshi Takahashi
Futoshi Takahashi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan, ([email protected])
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Abstract

We consider the problem −Δu = c0K(x)upε, u > 0 in Ω, u = 0 on δΩ, where Ω is a smooth, bounded domain in ℝN, N ≥ 3, c0 = N(N − 2), pε = (N + 2)/(N − 2) − ε and K is a smooth, positive function on . We prove that least-energy solutions of the above problem are non-degenerate for small ε > 0 under some assumptions on the coefficient function K. This is a generalization of the recent result by Grossi for K ≡ 1, and needs precise estimates and a new argument.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 203 - 222
Copyright
Copyright © Royal Society of Edinburgh 2010

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