A multiplicity result for a class of fractional p-Laplacian equations with perturbations in ℝN

Abstract

ABSTRACTThis paper deals with a class of nonlinear elliptic equations with perturbations in the whole space involving the fractional p-Laplacian. As a particular case, we investigate the following Schrödinger equations with perturbations: where is the fractional p-Laplacian operator, is a positive continuous function, is a perturbation. We first establish a compactness theorem which allows us to give some estimates of the energy levels where the Palais-Smale condition can fail. Furthermore, using Ekeland's variational principle and the mountain pass theorem, we obtain the existence of at least two distinct nonnegative weak solutions for the above-mentioned equations.