Multiple semiclassical solutions for the nonlinear Maxwell–Schrödinger system

In this paper we study the Maxwell–Schrödinger system in the three-dimensional space (MS)ε{−ε2Δu+V(x)u+ϕu=f(x,u),inR3,−Δϕ=4πu2,inR3. Under suitable assumptions on V(x)V(x) and f(x,u)f(x,u), we prove the existence and multiplicity of semiclassical solutions for problem (MS)ε(MS)ε by variational methods.