Infinitely Many Sign-Changing Solutions for the Nonlinear Schrödinger-Poisson System with Super 2-linear Growth at Infinity

Abstract

In this paper, we investigate the sign-changing solutions to the following Schrödinger-Poisson system $$\begin{aligned} \qquad \left\{ \begin{array}{ll} -\Delta u+V(x)u+\lambda \phi (x) u =f(u),\ \ \ &{}\ x \in {\mathbb {R}}^{3},\\ -\Delta \phi =u^2, \ \ \ &{}\ x \in {\mathbb {R}}^{3}, \\ \end{array} \right. \end{aligned}$$ where $$\lambda >0$$ is a parameter and f is super 2-linear at infinity. By using the method of invariant sets of descending flow and a multiple critical points theorem, we prove that this system possesses infinitely many sign-changing solutions for any $$\lambda >0$$ .