Infinitely many solutions for nonlinear Schrödinger equations with electromagnetic fields

In this paper, we study the nonlinear Schrödinger equation with electromagnetic fields(∇i−A(|y|))2u+V(|y|)u=|u|p−1u,u:RN↦C, where the vector A(r)=(A1(r),A2(r),…,AN(r))A(r)=(A1(r),A2(r),…,AN(r)) is such that Aj(r)Aj(r) (j=1,2,…,Nj=1,2,…,N) is a real function on R+R+ and V(r)V(r) is a positive function on R+R+, 1