Multiple solutions for a nonlinear Schrödinger–Poisson system with sign-changing potential

Abstract

This paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear Schrödinger–Poisson system. Under some suitable conditions, some criteria on the existence of nontrivial solutions, including a ground state solution, two solutions and a sequence of nontrivial solutions {uk} with ‖uk‖→0 as k→+∞, is established by applying the Morse theory and variational methods. Some known results in the literatures are extended and improved.