Infinitely many sign-changing solutions for the nonlinear Schr\"{o}dinger-Poisson system

Abstract

We investigate the existence of multiple bound state solutions, in particular sign-changing solutions. By using the method of invariant sets of descending flow, we prove that this system has infinitely many sign-changing solutions. In particular, the nonlinear term includes the power-type nonlinearity $f(u)=|u|^{p-2}u$ for the well-studied case $p\in(4,6)$, and the less-studied case $p\in(3,4)$, and for the latter case few existence results are available in the literature.