ON THE HESSIAN OF THE ENERGY FORM IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY

Abstract

The purpose of this work is to study the stability of radial solutions of degree d for the Ginzburg–Landau model of superconductivity with an applied magnetic field in a disk of radius [Formula: see text]. We consider the branch of solutions introduced in [24] as a branch with the radius of the ball as parameter. We prove that for small radii the branch is stable while it is unstable for large radii, see [6]. We then study in detail the Hessian of the energy at the symmetric vortex at the stability transition. Finally under a couple of extra assumptions, we construct a branch of solutions bifurcating from the radial one at this point, and describe it.