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arXiv · 2203.08660

A Liouville type result and quantization effects on the system $-Δu = u J'(1-|u|^{2})$ for a potential convex near zero

U. De Maio·R. Hadiji·C. Lefter·C. Perugia
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Abstract

We consider a Ginzburg-Landau type equation in $\R^2$ of the form $-Δu = u J'(1-|u|^{2})$ 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 \cite{BMR} 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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U. De Maio, R. Hadiji, C. Lefter, C. Perugia. 2022-11-14. A Liouville type result and quantization effects on the system $-Δu = u J'(1-|u|^{2})$ for a potential convex near zero. https://arxiv.org/abs/2203.08660

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