Stationary states for nonlinear Dirac equations with superlinear nonlinearities

Abstract

In this paper we consider the nonlinear Dirac equation $$ -i\partial_t\psi=ic\hbar\sum^3_{k=1}\alpha_k\partial_k\psi-mc^2\beta\psi+ G_\psi(x,\psi). $$ Under suitable superlinear assumptions on the nonlinearities we can obtain the existence of at least one stationary state for the equation by applying a generalized linking theorem.