Comptes Rendus
no. 6
Partial differential equations
Stability for entire radial solutions to the biharmonic equation with negative exponents
[Stabilité des solutions radiales entières de l'équation biharmonique avec exposants négatifs]

Présenté par : Haïm Brézis

Xia Huang1 ; Dong Ye2 ; Feng Zhou1
1 Center for Partial Differential Equations, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China
2 IECL, UMR 7502, Département de mathématiques, Université de Lorraine, 3, rue Augustin-Fresnel, 57073 Metz, France
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 632-636.

Dans cette note, on s'intéresse aux solutions radiales entières de l'équation semilinéaire biharmonique

Δ2u=−u−p,u>0dansRN,
où p>0 et N≥3. En particulier, on étudie la stabilité en dehors d'un compact des solutions radiales entières, et on résout un cas ouvert dans [5].

In this note, we are interested in entire solutions to the semilinear biharmonic equation

Δ2u=−u−p,u>0inRN,
where p>0 and N≥3. In particular, the stability outside a compact set of the entire radial solutions will be completely studied, which resolves the remaining case in [5].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.05.001
Xia Huang 1 ; Dong Ye 2 ; Feng Zhou 1

1 Center for Partial Differential Equations, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China
2 IECL, UMR 7502, Département de mathématiques, Université de Lorraine, 3, rue Augustin-Fresnel, 57073 Metz, France 
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Xia Huang; Dong Ye; Feng Zhou. Stability for entire radial solutions to the biharmonic equation with negative exponents. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 632-636. doi : 10.1016/j.crma.2018.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.05.001/

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