On a variational degenerate elliptic problem

Abstract.

In this paper we study a class of variational degenerate elliptic problems of the form $-div(a(x)\nabla u) = f(x,u)$ in $\Omega, u=0$ on $\delta\Omega$, where $\Omega$is a bounded or unbounded domain in ${\Bbb R}^n, n \ge 2$