Existence and asymptotic behavior of solutions for a Schrödinger-Born-Infeld system in R3 with a general nonlinearity

In this paper, we are concerned with the following Schrödinger-Born-Infeld system in R3{−Δu+u+λϕu=f(u),x∈R3,−div(∇ϕ1−|∇ϕ|2)=λu2,x∈R3,u(x)→0,ϕ(x)→0,as|x|→∞, where λ is a positive parameter, f∈C1(R,R) is a general nonlinearity introduced by Berestycki and Lions. The existence of nontrivial solutions for small λ and the asymptotic behavior of these solutions as λ tends to zero are established by variational methods.