Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 33, pp. 1-10.

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

Author: Kewei Zhang (Macquarie Univ., Sydney, Australia)

Abstract: 
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 
 $p> (n+1)/(n-3)$.
 
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.