Multiple positive solutions for Schrodinger-Poisson systems involving concave-convex nonlinearities

Abstract

In this article, we study the existence of multiple positive solutions for Schrödinger-Poisson systems involving concave-convex nonlinearities and sign-changing weight potentials. With the help of Nehari manifold and Ljusternik-Schnirelmann category theory, we investigate how the coefficient g(x) of the critical nonlinearity affects the number of positive solutions. Furthermore, we obtain a relationship between the number of positive solutions and the topology of the global maximum set of g.