Singularities in elliptic systems with absorption terms
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 229-271.
@article{ASNSP_1999_4_28_2_229_0,
author = {Bidaut-Veron, Marie-Fran\c coise and Grillot, Philippe},
title = {Singularities in elliptic systems with absorption terms},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {229--271},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 28},
number = {2},
year = {1999},
zbl = {0941.35018},
mrnumber = {1736228},
language = {en},
url = {archive.numdam.org/item/ASNSP_1999_4_28_2_229_0/}
}
Bidaut-Veron, Marie-Françoise; Grillot, Philippe. Singularities in elliptic systems with absorption terms. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 229-271. http://archive.numdam.org/item/ASNSP_1999_4_28_2_229_0/

[1] P. Aviles, On isolated singularities in some nonlinear partial differential equations, Indiana Univ. Math. J. 35 (1983), 773-79. | MR 711867 | Zbl 0548.35042

[2] M. Berger - P. Gauduchon - P. Mazet, "Le spectre d'une variété riemannienne", Lect. Notes Math., 194, Berlin, Heidelberg, New-York, Springer Ed. 1971. | Zbl 0223.53034

[3] M-F. Bidaut-Véron, Local behaviour of solutions of a class of nonlinear elliptic systems, Adv. Differential Equations (to appear). | MR 1734540 | Zbl 1005.35037

[4] M-F. Bidaut-Véron - L. Véron, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math. 106 (1991), 489-539. | MR 1134481 | Zbl 0755.35036

[5] M-F. Bidaut-Véron - P. Grillot, Asymptotic behaviour of the solutions of sublinear elliptic equations with a potential, Appl. Anal. (to appear). | MR 1688856 | Zbl 1034.35030

[6] M-F. Bidaut-Véron - V. Galaktionov - P. Grillot - L. Véron, Singularities for a 2-dimensional semilinear elliptic equation with a non-Lipschitz linearity, J. Differential Equations (to appear). | MR 1691075 | Zbl 0927.35037

[7] M-F. Bidaut- Véron - T. Raoux, Asymptotics of solutions of some nonlinear elliptic systems, Comm. Partial Differential Equations 21 (1996), 1035-1086. | MR 1399190 | Zbl 0932.35075

[8] H. Brézis - L. Véron,, Removable singularities of some nonlinear elliptic equations, Arc. Rat. Mech. Anal. 75 (1980), 1-6. | MR 592099 | Zbl 0459.35032

[9] D. De Figueiredo - P. Felmer, A Liouville-type theorem for elliptic systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 21 (1994), 387-397. | Numdam | MR 1310633 | Zbl 0820.35042

[10] D. De Figueiredo - P. Felmer, On superquadratic elliptic systems, Trans. Amer. Math. Soc. 343 (1994), 99-116. | MR 1214781 | Zbl 0799.35063

[11] M. Garcia - R. Manasevitch - E. Mitidieri - C. Yarur, Existence and nonexistence of singular positive solutions for a class of semilinear elliptic systems, Arch. Rat. Mech. Anal. 140 (1997), 253-284. | MR 1486894 | Zbl 0896.35038

[12] B. Gidas - J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981), 525-598. | MR 615628 | Zbl 0465.35003

[13] P. Grillot, Thèse de Doctorat, Université de Tours (1997).

[14] B. Guerch - L. Véron, Local properties of stationary solutions of some nonlinear singular Schrödinger equations, Rev. Mat. Iberoamericana 7 (1991), 65-114. | MR 1109481 | Zbl 0739.35016

[15] M. Herrero - J. Velazquez, On the dynamics of a semilinear heat equation with absorption, Comm. Partial Differential Equations 14 (1989), 1653-1715. | MR 1039914 | Zbl 0697.35019

[16] J. Hulshof - R. Van Der Vorst, Asymptotic behaviour of ground states, Proc. Amer. Math. Soc. 124 (1996), 2423-2431. | MR 1363170 | Zbl 0860.35029

[17] J. Serrin - H. Zou, Non-existence of positive solutions for the Lane-Emden system, Differential Integral Equations 9 (1996), 635-653. | MR 1401429 | Zbl 0868.35032

[18] J. Serrin - H. Zou, Existence of positive solutions of the Lane-Emden system, Atti Sem. Mat. Univ. Modena (1997), to appear. | MR 1645728 | Zbl 0917.35031

[19] L. Simon, Isolated singularities of extrema of geometric variational problems, In: "Harmonic Mappings and Minimal Immersions", Lecture Notes Math., 1161 (1985), 206-277. | MR 821971 | Zbl 0583.49028

[20] L. Véron, Comportement asymptotique des solutions d'équations elliptiques semilinéaires dans RN, Ann. Mat. Pura Appl. 127 (1981), 25-50. | MR 633393 | Zbl 0467.35013

[21] L. Véron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal. 5 (1981), 225-242. | MR 607806 | Zbl 0457.35031

[22] L. Véron, "Singularities of solutions of second order quasilinear equations", Pitman Research Notes in Math. Series, Longman (1996). | MR 1424468 | Zbl 0858.35018

[23] R. Van Der Vorst, "Variational problems with a strongly definite structure", Thesis, Leiden University (1994).

[24] C. Yarur, "Singularidades de ecuaciones de Schrödinger estacionarias", Tesis doctoral, Univ. Complutense, Madrid (1984).

[25] C. Yarur, Nonexistence of positive solutions for a class of semilinear elliptic systems, Europ. J. Differential Equations 8 (1996), 1-22. | MR 1405040 | Zbl 0853.35038