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

This paper is concerned with the following Klein-Gordon equation with sublinear nonlinearity coupled with Born-Infeld theory: -Delta u+V(x)u-2 omega+phi)phi u=f(x,u),x is an element of R3,Delta phi+beta Delta 4 phi=4 pi(omega+phi)u2,x is an element of R3. Delta f + beta Delta(4)f = 4p(omega + f)u2, 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.