Standing wave solutions of Maxwell-Dirac systems

This paper is concerned with the following Maxwell-Dirac system alpha k partial derivative ku+(V(x)+a)beta u+omega u-K(x)phi u=Fu(x,u),in R3, where V(x) is a potential function and F(x, u) is a nonlinear function modeling various types of interaction and K(t, x) is the varying pointwise charge distribution. Since the effects of the nonlocal term, we use some special techniques to deal with the nonlocal term. Moreover, we prove the existence of infinitely many geometrically distinct solutions for superquadratic as asymptotically quadtratic nonlinearities via variational approach. Some recent results in the literature are generalized and significantly improved. Some examples are also given to illustrate our main theoretical results.