Least energy sign-changing solutions for Kirchhoff-Schrödinger-Poisson system on bounded domains.

We investigate the following nonlinear system { − (a + b ∫ Ω | ∇ u | 2 d x) Δ u + ϕ u = λ u + μ | u | 2 u , x ∈ Ω , − Δ ϕ = u 2 , x ∈ Ω , u = ϕ = 0 , x ∈ ∂ Ω , with a , b > 0 , λ , μ ∈ R , and Ω ⊂ R 3 is bounded with smooth boundary. Let λ 1 > 0 be the first eigenvalue of (− Δ u , H 0 1 (Ω)). We get that for certain μ ~ > 0 there exists at least one least energy sign-changing solution for the above system if λ < a λ 1 and μ > μ ~ . In addition, we remark that the nonlinearity λ u + μ | u | 2 u does not satisfy the growth conditions. [ABSTRACT FROM AUTHOR]