We prove existence results for complex-valued solutions for a semilinear Schrödinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory, developed in [1, 2, 5].
"Single-peaks for a magnetic Schrödinger equation with critical growth." Adv. Differential Equations 11 (10) 1135 - 1166, 2006.