Elliptic problems with critical exponents and Hardy potentials

Journal of Differential Equations

Volumn 190, Issue 2, 2003, Pages 524-538

  Ruiz, D ^a   Willem, M ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Concentration compactness; Critical Sobolev exponent; Hardy inequality; Principle of Symmetric Criticality

Indexed keywords

EID: 0037845161     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(02)00178-X     Document Type: Article

References (10)

1. G. Bianchi, J. Chabrowski, A. Szulkin, On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent, Nonlinear Anal. TMA 25 (1995) 41-59.
2. H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983) 437-477.
3. A. Ferrero, F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177 (2001) 494-522.
4. J.P. Garcia Azorero, I. Peral Alonso, Hardy inequalities and some critical elliptic and parabolic problems, J. Differential Equations 144 (1998) 441-476.
5. G. Hardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge, UK, 1934.
6. E. Jannelli, The role played by space dimension in elliptic critical problems, J. Differential Equations 156 (1999) 407-426.
7. P.L. Lions, The concentration-compactness principle in the Calculus of Variations, The limit case, part 2, Rev. Mat. Iberoamericana 1 (1985) 45-121.
8. M. Ramos, Z-Q. Wang, M. Willem, Positive solutions for elliptic equations with critical growth in unbounded domains, Calculus of Variations and Differential Equations, Chapman & Hall/CRC Press, Boca Raton, 2000, pp. 192-199.
9. S. Wang, The existence of positive solution of semilinear elliptic equations with limiting Sobolev exponent, Proc. Roy. Soc. Edinburgh 117A (1991) 75-88.
10. M. Willem, Minimax Theorems, Birkhauser, Boston, Basel, Berlin, 1996.