Comptes Rendus
Équations aux dérivées partielles elliptiques
A Liouville theorem for the fractional Ginzburg–Landau equation
Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 727-731.

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation

u(x)= n u(1-|u| 2 ) |x-y| n-α dy,

where u: n k with k1 and 1<α<n/2. We prove that uL 2 ( n )u0 on n , as long as u is a bounded and differentiable solution.

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DOI : 10.5802/crmath.91
Classification : 45G05, 45E10, 35Q56, 35R11
Yayun Li 1 ; Qinghua Chen 2 ; Yutian Lei 2

1 School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing, 210023, China
2 Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Yayun Li and Qinghua Chen and Yutian Lei},
     title = {A {Liouville} theorem for the fractional {Ginzburg{\textendash}Landau} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {727--731},
     publisher = {Acad\'emie des sciences, Paris},
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     number = {6},
     year = {2020},
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     language = {en},
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Yayun Li; Qinghua Chen; Yutian Lei. A Liouville theorem for the fractional Ginzburg–Landau equation. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 727-731. doi : 10.5802/crmath.91. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.91/

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