Stationary solutions for a superlinear Dirac equation (Q2802673)

The authors consider the non-homogeneous Dirac equation NEWLINE\[NEWLINE -i\sum_{k=1}^3\alpha_k\partial_ku+a\beta u+M(x)u=F_u(x,u), NEWLINE\]NEWLINE where the right-hand side is a non-linear function, and \(M(x)\) corresponds to some potential, with respect to an existence of at least one its solution for some relatively non-restrictive conditions stated for \(F(x,u)\). In addition, it is shown that such a solution (or a set of solutions) is directly connected with minimizing of the energy functional, which is provided and discussed as well.