Resumo

In this paper we study the existence and multiplicity of solutions for the following class of nonlinear Dirac equations
\[
-i\epsilon \sum_{k=1}^{3} \alpha_k \partial_k u + a\beta u + V(x)u = f(|u|)u, \quad \text{in } \mathbb{R}^3,
\]
where \(V: \mathbb{R}^3 \to \mathbb{R}\) and \(f: [0, +\infty) \to \mathbb{R}\) are continuous functions. It is proved that the number of solutions is at least the number of global minimum points of V when \(\epsilon\) is small enough.