Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system

Abstract

In this paper, we consider the fractional subcritical Klein-Gordon-Maxwell system as follows: $$\begin{aligned} \left\{ \begin{aligned}&(-\Delta )^{s} u+V(x)u-(2\omega +\phi (x) )\phi (x)u= f(x,u), \,\,\,&\text {in } \mathbb {R}^3, \\&(\Delta )^{s} \phi (x)=(\omega +\phi (x) )u^2, \,\,\,&\text {in } \mathbb {R}^3, \end{aligned} \right. \end{aligned}$$the nonlinearity f is superlinear at infinity with subcritical growth and V is continuous and coercive. For the case when f is odd in u we obtain infinitely many high energy sign-changing solutions for the above problem by using a combination of invariant sets method and the Ljusternik-Schnirelman type minimax method.