Infinitely Many Solutions for the Klein–Gordon Equation with Sublinear Nonlinearity Coupled with Born–Infeld Theory

Abstract

This paper is concerned with the following Klein–Gordon equation with sublinear nonlinearity coupled with Born–Infeld theory: $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\Delta u+ V(x)u-(2\omega +\phi )\phi u=f(x,u), &{}\quad x\in {\mathbb {R}}^{3},\\ \Delta \phi +\beta \Delta _{4}\phi =4\pi (\omega +\phi )u^{2},&{}\quad x\in {\mathbb {R}}^{3}. \end{array} \right. \end{aligned}$$ Under some appropriate assumptions on V(x) and f(x, u), we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are improved and extended.