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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness of the least-energy solution
for a semilinear Neumann problem


Author: Massimo Grossi
Journal: Proc. Amer. Math. Soc. 128 (2000), 1665-1672
MSC (1991): Primary 35J70
Published electronically: October 18, 1999
MathSciNet review: 1694340
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Abstract: We prove that the least-energy solution of the problem

\begin{displaymath}\left\{ \begin{array}{ll} -d\Delta u+u=u^p\quad&\mbox{ in }B,\\ u>0\quad&\mbox{ in }B,\\ {{\partial u}\over{\partial\nu}}=0\quad&\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 $N\ge 3$, $p>1$ if $N=2$, is unique (up to rotation) if $d$ is small enough.


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Additional Information

Massimo Grossi
Affiliation: Dipartimento di Matematica, Università di Roma “La Sapienza", P.le A. Moro 2, 00185, Roma, Italy
Email: grossi@mat.uniroma1.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05491-X
PII: S 0002-9939(99)05491-X
Keywords: Uniqueness results, semilinear elliptic equations, Neumann problem
Received by editor(s): July 9, 1998
Published electronically: October 18, 1999
Additional Notes: This research was supported by M.U.R.S.T. (Project “Metodi Variazionali ed Equazioni Differenziali Non Lineari”)
Communicated by: Lesley M. Sibner
Article copyright: © Copyright 2000 American Mathematical Society