[Sur la trichotomie des solutions positives singulières associées à l'opérateur de Hardy–Sobolev]
In this Note, we present a complete classification of singularities of positive solutions of the equation
Dans cette Note, nous présentons une classification complète des singularités de solutions positives de l'équation
Accepté le :
Publié le :
Nirmalendu Chaudhuri 1 ; Florica C. Cîrstea 2
@article{CRMATH_2009__347_3-4_153_0, author = {Nirmalendu Chaudhuri and Florica C. C{\^\i}rstea}, title = {On trichotomy of positive singular solutions associated with the {Hardy{\textendash}Sobolev} operator}, journal = {Comptes Rendus. Math\'ematique}, pages = {153--158}, publisher = {Elsevier}, volume = {347}, number = {3-4}, year = {2009}, doi = {10.1016/j.crma.2008.12.018}, language = {en}, }
TY - JOUR AU - Nirmalendu Chaudhuri AU - Florica C. Cîrstea TI - On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator JO - Comptes Rendus. Mathématique PY - 2009 SP - 153 EP - 158 VL - 347 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2008.12.018 LA - en ID - CRMATH_2009__347_3-4_153_0 ER -
Nirmalendu Chaudhuri; Florica C. Cîrstea. On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 153-158. doi : 10.1016/j.crma.2008.12.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.018/
[1] An improved Hardy–Sobolev inequality and its application, Proc. Amer. Math. Soc., Volume 130 (2002), pp. 489-505
[2] Singular solutions for some semilinear elliptic equations, Arch. Rational Mech. Anal., Volume 99 (1987), pp. 249-259
[3] Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid, Volume 10 (1997), pp. 443-469
[4] Removable singularities of some nonlinear elliptic equations, Arch. Rational Mech. Anal., Volume 75 (1980), pp. 1-6
[5] N. Chaudhuri, F.C. Cîrstea, On classification of isolated singularities of solutions associated with the Hardy–Sobolev operator, in preparation
[6] Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Funct. Anal., Volume 250 (2007), pp. 317-346
[7] Extremal singular solutions for degenerate logistic-type equations in anisotropic media, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 119-124
[8] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983
[9] Local properties of stationary solutions of some nonlinear singular Schrödinger equations, Rev. Mat. Iberoamericana, Volume 7 (1991), pp. 65-114
[10] The strong maximum principle revisited, J. Differential Equations, Volume 196 (2004), pp. 1-66
[11] Regularly Varying Functions, Lecture Notes in Math., vol. 508, Springer-Verlag, Berlin, Heidelberg, 1976
[12] Singular solutions of some nonlinear elliptic equations, Nonlinear Anal. T.M.A., Volume 5 (1981), pp. 225-242
[13] Weak and strong singularities of nonlinear elliptic equations, Berkeley, CA, 1983 (Proc. Sympos. Pure Math.), Volume vol. 45, Amer. Math. Soc., Providence, RI (1986), pp. 477-795
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Cité par 17 documents. Sources : zbMATH
☆ This work were partially supported by an Australian Research Council Grant of Professors Neil Trudinger and Xu-Jia Wang.
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