Semiclassical solutions for a class of Schrِdinger system with magnetic potentials

This paper is concerned with the following nonlinear Schrödinger system with magnetic potentials { ( − i ε ∇ + A ( x ) ) 2 u + V ( x ) u = H u ( x , u , v ) , x ∈ R N , ( − i ε ∇ + A ( x ) ) 2 v + V ( x ) v = − H v ( x , u , v ) , x ∈ R N , where N ⩾ 3 , ε is a small parameter, A : R N → R N is the magnetic vector potential and V : R N → R is the electric potential. By applying generalized linking theorems for strongly indefinite functionals, we establish the existence and multiplicity of semiclassical solutions for superquadratic and subcritical nonlinearity.