On the existence and multiplicity of solutions to a Schrödinger–Kirchhoff–Poisson system with superlinear terms

This paper is concerned with the existence and multiplicity of solutions to the following Schrödinger–Kirchhoff–Poisson system − ( a + b ∫ Ω | ∇ u | 2 ) Δ u + K ( x ) ϕ u = f ( x , u ) , x ∈ Ω , − Δ ϕ = K ( x ) u 2 , x ∈ Ω , u = ϕ = 0 , x ∈ ∂ Ω , where a ≥ 0 and b > 0 and Ω is a bounded smooth domain of R 3 . Under certain assumptions of nonnegative density charge K ( x ) and superlinear term f ( x , u ) , we establish the existence of infinitely many nontrivial solutions by means of the symmetric mountain pass theorem.