Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system

In this paper, we study the following system -ε2v + V (x)v + ψ(x)v = vp, x ε R3, -Δψ=1/εv 2,lim |ψ|(x)=0, x ε R3, where ε ≥ 0, p ε (3; 5), V is positive potential. We relate the number of solutions with topology of the set where V attain their minimum value. By applying Ljusternik-Schnirelmann theory, we prove the multiplicity of solutions