## Stable solutions of the Ginzburg-Landau equation with magnetic field. (Solutions stables de l’équation de Ginzburg-Landau en présence de champ magnétique.)(French. Abridged English version)Zbl 0913.35134

Summary: We study the Ginzburg-Landau equation near the first critical value of the magnetic field $$H_{c_1}$$. We prove an estimate of this value, and we find branches of stable solutions of the equation for which we show that vortices appear while passing $$H_{c_1}$$.

### MSC:

 35Q60 PDEs in connection with optics and electromagnetic theory 82D55 Statistical mechanics of superconductors 35R35 Free boundary problems for PDEs
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