Small perturbations for nonlinear Schrödinger equations with magnetic potential (Q2027289)

In this paper, the authors study the qualitative analysis of solutions for three classes of nonlinear problems driven by the magnetic Laplace operator, where two equations are studied on bounded domains (under Dirichlet boundary condition) while the third problem is on the entire Euclidean space. They deduced that if a certain perturbation is sufficiently small in a prescribed sense, then the problems have at least two distinct solutions in a related magnetic Sobolev space. The proofs is based on variational, topological and analytic methods.