Symmetry of positive solutions of an almost-critical problem in an annulus期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Symmetry of positive solutions of an almost-critical problem in an annulus

Authors:	Daniele Castorina Filomena Pacella

Institution:	(1) Dipartimento di Matematica, Universitá di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy

Abstract:	We consider the subcritical problem $(I) \left\{ \begin{array}{clll} -\Delta u & = & N(N-2) u^{p - \epsilon} & \qquad\textrm{in} A\\ u & > & 0 & \qquad\textrm{in} A\\ u & = & 0 & \qquad\textrm{on} \delta A\\ \end{array} \right.$ where A is an annulus in $\mathbb{R}^N$ , $N \geq 3$ , $p + 1 = \frac{2N}{N-2}$ is the critical Sobolev exponent and $\epsilon > 0$ is a small parameter. We prove that solutions of (I) which concentrate at one or two points are axially symmetric.Received: 7 July 2003, Accepted: 10 May 2004, Published online: 16 July 2004Filomena Pacella: Research supported by MIUR, project Variational Methods and Nonlinear Differential Equations.

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