Existence of infinitely many solutions to a class of Kirchhoff–Schrödinger–Poisson system

摘要

In this paper, we consider the existence of infinitely many solutions to following nonlinear Kirchhoff–Schrödinger–Poisson systema+b∫R3|∇u|2+V(x)u2-Δu+V(x)u+λl(x)ϕu=f(x,u),x∈R3,-Δϕ=λl(x)u2,x∈R3,where constants a>0,b⩾0 and λ⩾0. When f has sublinear growth in u, we obtain infinitely many solutions under certain assumption that V do not have a positive lower bound. The technique we use in this paper is the symmetric mountain pass theorem established by Kajikiya (2005).