Infinitely many sign-changing solutions for planar Schrödinger-Poisson system

In this paper, we consider the following planar Schr & ouml;dinger-Poisson system \[ \left\{ \begin{aligned} & -\Delta u +V(x)u + \phi u=|u|<^>{q-2}u,\ {\rm in} \ \mathbb{R}<^>2,\cr & \Delta \phi =u<^>2 ,\ {\rm in}\ \mathbb{R}<^>2, \end{aligned}\right. \]{-Delta u+V(x)u+phi u=|u|q-2u,inR2,Delta phi=u2,inR2, where the potential $ V:\mathbb {R}<^>2\to \mathbb {R} $ V:R2 -> R is continuous and coercive. By using the method of perturbation and invariant sets of descending flow, we obtain the existence of infinitely many sign-changing solutions for this system.