On the stability of radial solutions of the Ginzburg-Landau equation (Q1893836)

Consider the following boundary value problem: \[ -\Delta u= {1\over \varepsilon^2} u(1- |u|^2)\quad\text{in} \quad G,\qquad u= g\quad\text{on} \quad \partial G. \] The author derives the stability of radial solutions for \(\varepsilon= 1\) and studies critical values of \(\varepsilon\) for the stability of radial solutions.