Infinitely many multi-vortex solutions of the magnetic Ginzburg–Landau equation with external potentials in R2

In this paper, we consider the magnetic Ginzburg–Landau equation with external potentials μV(x) for the type II superconductors. We prove, by reduction arguments, that under suitable conditions on V(x), the magnetic Ginzburg–Landau equation with external potentials in R2 has infinitely many multi-vortex solutions for μ > 0 being sufficiently small.