A multiplicity result for singular NLS equations with magnetic potentials

In this paper, we obtain multiple solutions u:RN→Cu:RN→C of the singular nonlinear Schrödinger equation with an external electromagnetic field equation(1)(ħi∇−A(x))2u+(V(x)−ε(ħ)W(x))u=|u|p−2ux∈RN, where N≥2N≥2, 2