Multiple positive solutions for a Schrödinger–Poisson–Slater system

Abstract: In this paper we investigate the existence of positive solutions to the following Schrödinger–Poisson–Slater system where Ω is a bounded domain in , λ is a fixed positive parameter and . We prove that if p is “near” the critical Sobolev exponent , then the number of positive solutions is greater then the Lusternik–Schnirelmann category of Ω. [Copyright &y& Elsevier]