A perturbation approach for the Schrödinger-Born-Infeld system: Solutions in the subcritical and critical case

In this paper, we study the following Schrödinger-Born-Infeld system with a general nonlinearity{−Δu+u+ϕu=f(u)+μ|u|4uinR3,−div(∇ϕ1−|∇ϕ|2)=u2inR3,u(x)→0,ϕ(x)→0,asx→∞, where μ≥0 and f∈C(R,R) satisfies suitable assumptions. This arises from coupling of nonlinear Schrödinger equation Born-Infeld theory. We use new perturbation approach to prove existence multiplicity nontrivial solutions above in subcritical critical case. emphasise that our results cover case f(u)=|u|p−1u for p∈(2,5/2] μ=0 which was left [2] as an open problem.