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We are concerned with the qualitative analysis of solutions for threeclasses of nonlinear problems driven by the magnetic Laplace operator. We aremainly interested in the perturbation effects created by two reaction terms withdifferent structure. Two equations are studied on bounded domains (under Dirichletboundary condition) while the third problem is on the entire Euclidean space.Our main results establish that if a certain perturbation is sufficiently small (ina prescribed sense) then the problems have at least two distinct solutions in arelated magnetic Sobolev space. The proofs combine variational, topological andanalytic methods.

Small Perturbations for Nonlinear Schrödinger Equations with Magnetic Potential