Electron. J. Diff. Eqns., Vol. 1999(1999), No. 33, pp. 1-10.

Uniqueness for a semilinear elliptic equation in non-contractive domains under supercritical growth conditions

Kewei Zhang (Macquarie University, Sydney, Australia)

We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in $\Bbb R^n$ and establish uniqueness results for the smooth solutions of the Dirichlet problem for
$-\Delta u+|u|^{p-1}u=0$.
We require the domain to be in $\Bbb R^n$ with $n \geq 4$ and with p greater than (n+1)/(n-3).

Submitted May 12, 1999. Published September 15, 1999.
Math Subject Classifications: 35J65, 35B05, 58E05.
Key Words: semilinear elliptic equation, supercritical growth, uniqueness, non-contractible domains, Pohozaev identity.

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Kewei Zhang
Department of Mathematics
Macquarie University
Sydney, Australia
e-mail address: kewei@ics.mq.edu.au

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