Existence of solution for a class of elliptic problems in exterior domain with discontinuous nonlinearity

In this paper, we study the existence of nontrivial solution for a class of elliptic problems of the form -Delta u + u = f(p,delta)(u(x)) a.e in Omega where Omega subset of R-N is an exterior domain for N > 2 and f(p,delta) : R -> R is an odd discontinuous function given by f(p),delta(t) = {t|t|(p-2), t is an element of[0,a], (1+delta)t|t|(p-2), t > a, with a > 0, delta > 0 and p is an element of(2, 2*;). For small enough delta and a, seeking help of the dual functional corresponding to the problem, we prove existence of at least one positive solution when R-N\Omega subset of B-sigma(0) for sufficiently small sigma.