The Brezis-Nirenberg problem near criticality in dimension 3

Journal des Mathematiques Pures et Appliquees

Volumn 83, Issue 12, 2004, Pages 1405-1456

  del Pino, Manuel ^a   Dolbeault, Jean ^b   Musso, Monica ^c  

^a UNIVERSITY OF CHILE   (Chile)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c POLITECNICO DI TORINO   (Italy)

Author keywords

Bubbling solutions; Finite dimensional reduction; Green's function

Indexed keywords

EID: 8644235096     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2004.02.007     Document Type: Article

References (25)

1. Adimurthi Pacella F. Yadava S.L. Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity J. Funct. Anal. 113 2 1993 318-350
2. Aubin T. Problèmes isopérimétriques et espaces de Sobolev J. Differential Geom. 11 4 1976 573-598
3. Bahri A. Coron J.M. On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain Comm. Pure Appl. Math. 41 3 1988 253-294
4. Bahri A. Li Y.-Y. Rey O. On a variational problem with lack of compactness: The topological effect of the critical points at infinity Calc. Var. Partial Differential Equations 3 1 1995 67-93
5. Brezis H. Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents Comm. Pure Appl. Math. 36 4 1983 437-477
6. Brezis H. Peletier L.A. Asymptotics for elliptic equations involving critical growth, in Partial Differential Equations and the Calculus of Variations, vol. I, in Progr. Nonlinear Differential Equations Appl. vol. 1 1989 149-192 Birkhäuser Boston
7. Budd C. Norbury J. Semilinear elliptic equations and supercritical growth J. Differential Equations 68 2 1987 169-197
8. Caffarelli L.A. Gidas B. Spruck J. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth Comm. Pure Appl. Math. 42 3 1989 271-297
9. n Comm. Partial Differential Equations 24 5-6 1999 785-799
10. del Pino M. Felmer P. Musso M. Two-bubble solutions in the super-critical Bahri-Coron's problem Calc. Var. Partial Differential Equations 16 2 2003 113-145
11. del Pino M. Dolbeault J. Musso M. "Bubble-tower" radial solutions in the slightly supercritical Brezis-Nirenberg problem J. Differential Equations 193 2 2003 280-306
12. M. del Pino, J. Dolbeault, M. Musso, A phase plane analysis of the "Multi-bubbling" phenomenon in some slightly supercritical equations, Monatshefte für Mathematik, in press
13. del Pino M. Felmer P. Semi-classical states for nonlinear Schrödinger equations J. Funct. Anal. 149 1 1997 245-265
14. Druet O. Elliptic equations with critical Sobolev exponents in dimension 3 Ann. Inst. H. Poincaré Anal. Non Linéaire 19 2 2002 125-142
15. Flucher M. Wei J. Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots Manuscripta Math. 94 3 1997 337-346
16. Fowler R.H. Further studies on Emden's and similar differential equations Quart. J. Math. 2 1931 259-288
17. Han Z.-C. Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent Ann. Inst. H. Poincaré Anal. Non Linéaire 8 2 1991 159-174
18. Ni W.-M. Pan X.B. Takagi I. Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents Duke Math. J. 67 1 1992 1-20
19. Pohozaev S. On the eigenfunctions of the equation Δu + λf (u) = 0 Dokl. Akad. Nauk SSSR 165 1965 36-39
20. Rey O. The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent J. Funct. Anal. 89 1 1990 1-52
21. Rey O. Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent Duke Math. J. 60 3 1990 815-861
22. Rey O. The topological impact of critical points at infinity in a variational problem with lack of compactness: The dimension 3 Adv. Differential Equations 4 4 1999 581-616
23. Rey O. The question of interior blow-up-points for an elliptic Neumann problem: The critical case J. Math. Pures Appl. (9) 81 7 2002 655-696
24. Talenti G. Best constant in Sobolev inequality Ann. Mat. Pura Appl. (IV) 110 1976 353-372
25. p = 0 in a ball Comm. Partial Differential Equations 17 7-8 1992 1141-1164