Sign-changing solutions for a Schrödinger–Kirchhoff–Poisson system with 4-sublinear growth nonlinearity

In this paper we consider the followingSchrödinger–Kirchhoff–Poisson-type system { − ( a + b ∫ Ω | ∇ u | 2 d x ) Δ u + λ ϕ u = Q ( x ) | u | p − 2 u in   Ω , − Δ ϕ = u 2 in   Ω , u = ϕ = 0 on   ∂ Ω , where Ω is abounded smooth domain of R 3 , a > 0 , b ≥ 0 are constantsand λ is a positive parameter. Under suitable conditions on Q ( x ) and combining the method of invariant sets of descending flow, we establishthe existence and multiplicity of sign-changing solutions to this problemfor the case that 2 < p < 4 as λ sufficient small. Furthermore,for λ = 1 and the above assumptions on Q ( x ) , we obtain the sameconclusions with 2 < p < 12 5 .