Partial Differential Equations
Comments on two Notes by L. Ma and X. Xu
[Commentaires sur deux Notes de L. Ma et X. Xu]

Présenté par : Haïm Brezis

Brezis, Haïm1
1 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 269-271.

Dans cette Note jʼapporte des corrections et des références supplémentaires à des assertions de L. Ma et X. Xu (2009) [6] et L. Ma (2010) [5].

In this Note I discuss some assertions made by L. Ma and X. Xu (2009) [6] and L. Ma (2010) [5], which need to be corrected and supplemented with additional references.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.024
Brezis, Haïm 1

1 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA 
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Brezis, Haïm. Comments on two Notes by L. Ma and X. Xu. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 269-271. doi : 10.1016/j.crma.2011.01.024. https://www.numdam.org/articles/10.1016/j.crma.2011.01.024/

[1] Brezis, H. Semilinear equations in RN without condition at infinity, Appl. Math. Optim., Volume 12 (1984), pp. 271-282

[2] Hervé, M.; Hervé, R.M. Quelques propriétés des solutions de lʼéquation de Ginzburg–Landau sur un ouvert de R2, Potential Anal., Volume 5 (1996), pp. 591-609

[3] Keller, J. On solutions to Δu=f(u), Comm. Pure Appl. Math., Volume 10 (1957), pp. 503-510

[4] Loewner, C.; Nirenberg, L. Partial differential equations invariant under conformal or projective transformations, Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, 1974, pp. 245-272

[5] Ma, L. Liouville type theorem and uniform bound for the Lichnerowicz equation and the Ginzburg–Landau equation, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 993-996

[6] Ma, L.; Xu, X. Uniform bound and a non-existence result for the Lichnerowicz equation in the whole n-space, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009), pp. 805-808

[7] Osserman, R. On the inequality Δu⩾f(u), Pac. J. Math., Volume 7 (1957), pp. 1641-1647

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