Comptes Rendus
no. 5-6
Partial Differential Equations
Comments on two Notes by L. Ma and X. Xu
Haïm Brezis
Haïm Brezis1
1Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 269-271

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.

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].

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.01.024

Haïm Brezis  1

1 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA 
Haïm Brezis. Comments on two Notes by L. Ma and X. Xu. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 269-271. doi: 10.1016/j.crma.2011.01.024
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[1] H. Brezis Semilinear equations in RN without condition at infinity, Appl. Math. Optim., Volume 12 (1984), pp. 271-282

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

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

[4] C. Loewner; L. Nirenberg 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] L. Ma 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] L. Ma; X. Xu 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] R. Osserman On the inequality Δu⩾f(u), Pac. J. Math., Volume 7 (1957), pp. 1641-1647

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