Local uniqueness of the magnetic Ginzburg-Landau equation

摘要

In this paper, we consider the magnetic Ginzburg-Landau equation: -Delta A psi+lambda 2(|psi|2-1)psi=0inR2, backward difference x backward difference xA+Im(psi over bar backward difference A psi)=0inR2,|psi|-> 1as|x|->+infinity,where lambda>1 is a coupling parameter, backward difference A= backward difference -iA and Delta A= backward difference A center dot backward difference A are, respectively, the covariant gradient and Laplacian. We prove, by perturbation arguments, that the only possible minimizer of the magnetic Ginzburg-Landau functional with degree 1 is the radial solution for lambda sufficiently close to 1.