Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations

In this paper, we study the nonrelativistic limit of the following nonlinear Dirac equations−icα⋅∇u+mc2βu−ωu+V(x)u=W(x)|u|p−2u, where c denotes the speed of light, m>0 is the mass of the electron. Then we show nonexistence of special solutions by using the nonrelativistic limit of the corresponding nonlinear Dirac equations. Here, nonexistence means no nontrivial solutions.