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On the stability of radial solutions of the Ginzburg-Landau equation. (English) Zbl 0839.35011
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.
Reviewer: A.Tsutsumi (Osaka)

##### MSC:
 35B35 Stability in context of PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations 35Q72 Other PDE from mechanics (MSC2000)