In this note we prove the non-existence of a positive solution for the 
nonlinear problem: $-\trip u=\lam u^q +W(x)u^r$ in $\Om$, $u=0$ on 
$\pO$, where $\lam >0$, $0\le q <r \le \frac{N+2}{N-2}$, 
$1<p\le \frac{2N}{N-2}$, $\Om$ is an unbounded domain in $\BRN$ ($N \ge 3$) 
with some properties and $W\in W^{1,\infty}(\Om )$.