We consider a Ginzburg-Landau type equation in R^2 of the form −∆u = uJ′(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. Rivìere from  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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