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Uniqueness of the least-energy solution for a semilinear Neumann problem
Authors:Massimo Grossi
Affiliation:Dipartimento di Matematica, Università di Roma ``La Sapienza", P.le A. Moro 2, 00185, Roma, Italy
Abstract:We prove that the least-energy solution of the problem

begin{displaymath}left{ begin{array}{ll} -dDelta u+u=u^pquad&mbox{ in }B, u>0quad&mbox{ in }B, {{partial u}over{partialnu}}=0quad&mbox{ on }partial B, end{array}right.end{displaymath}

where $B$ is a ball, $d>0$ and $1<p<{{N+2}over{N-2}}$ if $Nge 3$, $p>1$ if $N=2$, is unique (up to rotation) if $d$ is small enough.

Keywords:Uniqueness results   semilinear elliptic equations   Neumann problem
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