single and multi-peak solutions for a nonlinear maxwell–schrödinger system with a general nonlinearity

for the following elliptic system in r³ −ε²δv + v(x)v + φ(x)v = f (v),

−δφ = v², lim_|x|→∞φ(x) = 0,

we construct positive solutions u and φ which concentrate at several given isolated local minimum components of v as ε → 0. the potential v is a strictly positive continuous function and the nonlinearity f is subcritical near infinity and superlinear near zero and satisfies only the berestycki–lions condition.