  In this paper, we are concerned with the multiplicity of nontrivial solutions
for the following class of complex problems $$ (-i\nabla - A(\mu x))^{2}u= \mu
|u|^{q-2}u + |u|^{2^{*}-2}u \ \mbox{in} \ \Omega, \ \ \ \ u \in
H^{1}_{0}(\Omega,\mathbb{C}), $$ where $\Omega \subset \mathbb{R}^{N} (N \geq
4)$ is a bounded domain with smooth boundary. Using the Lusternik-Schnirelman
theory, we relate the number of solutions with the topology of $\Omega$.
