July/August 2023 A Liouville type result and quantization effects on the system $-\Delta u = u J'(1-|u|^{2})$ for a potential convex near zero
Umberto De Maio, Rejeb Hadiji, Catalin Lefter, Carmen Perugia
Adv. Differential Equations 28(7/8): 613-636 (July/August 2023). DOI: 10.57262/ade028-0708-613

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.

Citation

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Umberto De Maio. Rejeb Hadiji. Catalin Lefter. Carmen Perugia. "A Liouville type result and quantization effects on the system $-\Delta u = u J'(1-|u|^{2})$ for a potential convex near zero." Adv. Differential Equations 28 (7/8) 613 - 636, July/August 2023. https://doi.org/10.57262/ade028-0708-613

Information

Published: July/August 2023
First available in Project Euclid: 10 April 2023

Digital Object Identifier: 10.57262/ade028-0708-613

Subjects:
Primary: 35B25 , 35J50 , 35J55 , 35Q40 , 35Q56

Rights: Copyright © 2023 Khayyam Publishing, Inc.

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Vol.28 • No. 7/8 • July/August 2023
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