Summary: | Abstract This paper deals with the following Kirchhoff–Schrödinger–Poisson system: { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u + ϕ u = K ( x ) f ( u ) in R 3 , − Δ ϕ = u 2 in R 3 , $$ \textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=K(x)f(u)&\text{in } \mathbb{R}^{3}, \\ -\Delta \phi =u^{2}&\text{in } \mathbb{R}^{3}, \end{cases} $$ where a, b are positive constants, K ( x ) $K(x)$ , V ( x ) $V(x)$ are positive continuous functions vanishing at infinity, and f ( u ) $f(u)$ is a continuous function. Using the Nehari manifold and variational methods, we prove that this problem has a least energy nodal solution. Furthermore, if f is an odd function, then we obtain that the equation has infinitely many nontrivial solutions.
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