  In this paper we consider the following class of elliptic problems $$-
\Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,$$ for $x \in
\mathbb{R}^N$, $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a
sign-changing weight function, $b_{\mu}(x)$ has some aditional conditions, $u
\in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow\mathbb{R}^N$ is a
magnetic potential. Exploring the Bahri Li argument and some preliminar results
we will discuss the existence of four solution to the problem in question.
