Single and multi-peak solutions for a nonlinear Maxwell–Schrödinger system with a general nonlinearity

For the following elliptic system in R3R3−ε2Δv+V(x)v+ϕ(x)v=f(v),−ε2Δv+V(x)v+ϕ(x)v=f(v),−Δϕ=v2,lim|x|→∞ϕ(x)=0, we construct positive solutions uu and ϕϕ which concentrate at several given isolated local minimum components of VV as ε→0ε→0. The potential VV is a strictly positive continuous function and the nonlinearity ff is subcritical near infinity and superlinear near zero and satisfies only the Berestycki–Lions condition.