Stable Solutions with Zeros to the Ginzburg–Landau Equation with Neumann Boundary Condition

This paper is devoted to the Ginzburg–Landau equationΔΦ+λ(1−Φ2) Φ=0,Φ=u1+iu2in a bounded domainΩ nwith the homogeneous Neumann boundary condition. The previous works [12–14] showed that for largeλthere exist stable non-constant solutions with no zeros in domains, which are topologically non-trivial in a certain sense. In this aritcle it is proved that for a domainΩcontaining a non-trivial domainDas a subset, there exist stable solutions with zeros provided that the volume ofΩ\Dis sufficiently small.