Existence of multiple solutions for modified Schrödinger–Kirchhoff–Poisson type systems via perturbation method with sign-changing potential

Abstract

In this paper, we prove the existence of positive solutions and negative solutions for the following modified Schrödinger–Kirchhoff–Poisson type systems {−(a+b∫R3∣∇u∣2)Δu+V(x)u+ϕu−12uΔ(u2)=f(x,u),inR3,−Δϕ=u2,inR3, where a>0, b≥0, V and f are continuous functions and V(x) is allowed to be sign-changing. Under some certain assumptions on V and f, we prove the existence of nontrivial nonnegative solutions, nontrivial nonpositive solutions and sequence of high energy solutions via the perturbation method.