Comptes Rendus
no. 5-6
Partial Differential Equations
Comments on two Notes by L. Ma and X. Xu
Presented by: 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 
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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

[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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