Nonrelativistic Limit of Ground State Solutions for Nonlinear Dirac-Klein-Gordon Systems

We study the nonrelativistic limit and some properties of the solutions(psi, ?) := (u, v, ?) is an element of C-2 x C-2 x Rfor the following nonlinear Dirac-Klein-Gordon systems: { ic sigma(3)(k=1) alpha(k)& part;(k)psi - mc(2)beta psi - omega psi- lambda?beta psi = |psi|(p-2)psi, {- ?? + c(2)M(2)? = 4 pi lambda(beta psi) middot psi,where p is an element of [(5)/(12), (3)/(8)], c denotes the speed of light, m > 0 is the mass of the electron. We show that the first component u and the last one ? of ground state solutions for nonlinear Dirac-Klein-Gordon systems converge to zero and the second one v converges to corresponding solutions of a coupled system of nonlinear Schrodinger equations as the speed of light tends to infinity for electrons with small mass. Moreover, we also prove the uniform boundedness and the exponential decay properties of the solutions for the nonlinear Dirac-Klein-Gordon systems with respect to the speed of light c.