Abstract
We consider a Ginzburg-Landau type equation in $\mathbb R^2$ of the form $-\Delta u = u J'(1-|u|^{2})$ with a potential function $J$ satisfying weak conditions allowing for example a zero of infinite order in the origin. We extend in this context the results concerning quantization of finite potential solutions of H. Brezis, F. Merle, T. Rivière from [10] who treat the case when $J$ behaves polinomially near $0,$ as well as a result of Th. Cazenave, found in the same reference, and concerning the form of finite energy solutions.
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