Existence and concentration of positive solutions for non-autonomous Schrödinger-Poisson systems

Abstract

In this paper, we deal with a class of non-autonomous Schrödinger-Poisson systems involving concave-convex nonlinearities and weight functions. We obtain the existence and multiplicity of positive solutions by a global compactness lemma of Schrödinger-Poisson type and Ljusternik-Schnirelmann theory. Moreover, we also conclude that the global maximum point of the solution concentrates on a local minimum point of the weight function.