Multiplicity of positive solutions for a class of Schrödinger-Poisson systems with critical growth

Abstract

We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Schrodinger-Poisson system where e > 0 is a parameter, V is a positive continuous potential bounded away from zero satisfying some conditions and f is a subcritical nonlinearity, 2 * = 6 is the critical Sobolev exponent in R 3 . We use a variational method to obtain the multiplicity of positive solutions by means of the Ljusternik-Schnirelmann category of the set where V attains its minimum value.