Singularities in elliptic systems with absorption terms

Marie-Françoise Bidaut-Veron; Philippe Grillot

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)

  • Volume: 28, Issue: 2, page 229-271
  • ISSN: 0391-173X

How to cite

top

Bidaut-Veron, Marie-Françoise, and Grillot, Philippe. "Singularities in elliptic systems with absorption terms." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.2 (1999): 229-271. <http://eudml.org/doc/84376>.

@article{Bidaut1999,
author = {Bidaut-Veron, Marie-Françoise, Grillot, Philippe},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {elliptic systems of PDE; singularities; anisotropic behaviour},
language = {eng},
number = {2},
pages = {229-271},
publisher = {Scuola normale superiore},
title = {Singularities in elliptic systems with absorption terms},
url = {http://eudml.org/doc/84376},
volume = {28},
year = {1999},
}

TY - JOUR
AU - Bidaut-Veron, Marie-Françoise
AU - Grillot, Philippe
TI - Singularities in elliptic systems with absorption terms
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 2
SP - 229
EP - 271
LA - eng
KW - elliptic systems of PDE; singularities; anisotropic behaviour
UR - http://eudml.org/doc/84376
ER -

References

top
  1. [1] P. Aviles, On isolated singularities in some nonlinear partial differential equations, Indiana Univ. Math. J.35 (1983), 773-79. Zbl0548.35042MR711867
  2. [2] M. Berger - P. Gauduchon - P. Mazet, "Le spectre d'une variété riemannienne", Lect. Notes Math., 194, Berlin, Heidelberg, New-York, Springer Ed. 1971. Zbl0223.53034
  3. [3] M-F. Bidaut-Véron, Local behaviour of solutions of a class of nonlinear elliptic systems, Adv. Differential Equations (to appear). Zbl1005.35037MR1734540
  4. [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. Zbl0755.35036MR1134481
  5. [5] M-F. Bidaut-Véron - P. Grillot, Asymptotic behaviour of the solutions of sublinear elliptic equations with a potential, Appl. Anal. (to appear). Zbl1034.35030MR1688856
  6. [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). Zbl0927.35037MR1691075
  7. [7] M-F. Bidaut- Véron - T. Raoux, Asymptotics of solutions of some nonlinear elliptic systems, Comm. Partial Differential Equations21 (1996), 1035-1086. Zbl0932.35075MR1399190
  8. [8] H. Brézis - L. Véron,, Removable singularities of some nonlinear elliptic equations, Arc. Rat. Mech. Anal.75 (1980), 1-6. Zbl0459.35032MR592099
  9. [9] D. De Figueiredo - P. Felmer, A Liouville-type theorem for elliptic systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci.21 (1994), 387-397. Zbl0820.35042MR1310633
  10. [10] D. De Figueiredo - P. Felmer, On superquadratic elliptic systems, Trans. Amer. Math. Soc.343 (1994), 99-116. Zbl0799.35063MR1214781
  11. [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. Zbl0896.35038MR1486894
  12. [12] B. Gidas - J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981), 525-598. Zbl0465.35003MR615628
  13. [13] P. Grillot, Thèse de Doctorat, Université de Tours (1997). 
  14. [14] B. Guerch - L. Véron, Local properties of stationary solutions of some nonlinear singular Schrödinger equations, Rev. Mat. Iberoamericana7 (1991), 65-114. Zbl0739.35016MR1109481
  15. [15] M. Herrero - J. Velazquez, On the dynamics of a semilinear heat equation with absorption, Comm. Partial Differential Equations14 (1989), 1653-1715. Zbl0697.35019MR1039914
  16. [16] J. Hulshof - R. Van Der Vorst, Asymptotic behaviour of ground states, Proc. Amer. Math. Soc.124 (1996), 2423-2431. Zbl0860.35029MR1363170
  17. [17] J. Serrin - H. Zou, Non-existence of positive solutions for the Lane-Emden system, Differential Integral Equations9 (1996), 635-653. Zbl0868.35032MR1401429
  18. [18] J. Serrin - H. Zou, Existence of positive solutions of the Lane-Emden system, Atti Sem. Mat. Univ. Modena (1997), to appear. Zbl0917.35031MR1645728
  19. [19] L. Simon, Isolated singularities of extrema of geometric variational problems, In: "Harmonic Mappings and Minimal Immersions", Lecture Notes Math., 1161 (1985), 206-277. Zbl0583.49028MR821971
  20. [20] L. Véron, Comportement asymptotique des solutions d'équations elliptiques semilinéaires dans RN, Ann. Mat. Pura Appl.127 (1981), 25-50. Zbl0467.35013MR633393
  21. [21] L. Véron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal.5 (1981), 225-242. Zbl0457.35031MR607806
  22. [22] L. Véron, "Singularities of solutions of second order quasilinear equations", Pitman Research Notes in Math. Series, Longman (1996). Zbl0858.35018MR1424468
  23. [23] R. Van Der Vorst, "Variational problems with a strongly definite structure", Thesis, Leiden University (1994). 
  24. [24] C. Yarur, "Singularidades de ecuaciones de Schrödinger estacionarias", Tesis doctoral, Univ. Complutense, Madrid (1984). 
  25. [25] C. Yarur, Nonexistence of positive solutions for a class of semilinear elliptic systems, Europ. J. Differential Equations8 (1996), 1-22. Zbl0853.35038

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.