Quasilinear elliptic problems in RN involving oscillatory nonlinearities

Abstract

In this paper we study an elliptic problem in R N which involves the p-Laplacian, p > N 2, and the nonlinear term has an oscillatory behavior. By means of a direct variational approach, we establish the existence of infinitely many homoclinic solutions whose W 1,p (R N )-norms tend to zero (to infinity, respectively) whenever the nonlinearity oscillates at zero (at infinity, respectively). The solutions have invariance properties with respect to certain subgroups of the orthogonal group O(N).