Abstract:

In this paper, we consider a Ginzburg-Landau functional for a complex vector order parameter $\Psi=[\psi_+, \psi_-]$. In particular, we consider entire solutions in all ${\Bbb R}^2$, which are obtained by blowing up around vortices. Among the entire solutions we distinguish those which are locally minimizing solutions, and we show that locally minimizing solutions must have degrees $n_\pm \in \{0, \pm1\}$. By studying the local structure of these solutions, we also show that one component of the solution vanishes, but the other does not, which describes the coreless vortex phenomenon in physics.

Key words: Elliptic systems, Locally minimizing solutions, Variational methods for elliptic systems