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

In this paper, we consider the existence of infinitely many solutions to following nonlinear Kirchhoff–Schrödinger–Poisson system a + b ∫ R 3 | ∇ u | 2 + V ( x ) u 2 - Δ u + V ( x ) u + λ l ( x ) ϕ u = f ( x , u ) , x ∈ R 3 , - Δ ϕ = λ l ( x ) u 2 , x ∈ R 3 , 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). [ABSTRACT FROM AUTHOR]