Quasi-linear equations in RN:: perturbation results

In this paper we prove existence of nontrivial solutions for the quasi-linear elliptic problem {div((I + epsilonA(x, u))delu) + u + epsilonH(x, u,delu) = \u\(p-1), in R-N, u is an element of H-1(R-N) boolean AND W-2,W-q (R-N), q > N where 1 < p < (N + 2)/(N - 2), N > 2 and the operator -div((I + epsilonA(x, u))delu) +epsilonH(x, u, delu) is a perturbation of the Laplacian. We use a perturbation method recently developed in [1], [2], [3] and we get results both in the variational and in the non-variational framework.