Stationary states for nonlinear Dirac equations with superlinear nonlinearities

Minbo Yang, Yanheng Ding

Abstract


In this paper we consider the nonlinear Dirac equation
$$
-i\pa_t\psi=ic\hbar\sum^3_{k=1}\alpha_k\partial_k\psi-mc^2\beta\psi+
G_\psi(x,\psi).
$$
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.

Keywords


Dirac equation; ground state solution; superlinear nonlinearities

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