### Stationary states for nonlinear Dirac equations with superlinear nonlinearities

#### 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.

$$

-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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