Multiple positive solutions for a class of nonlinear elliptic equations

Journal of Mathematical Analysis and Applications

Volumn 295, Issue 2, 2004, Pages 341-354

  Chen, Jianqing ^a  

^a FUJIAN NORMAL UNIVERSITY   (China)

Author keywords

Critical Hardy Sobolev exponent; Exact local behavior; Multiple positive solutions

Indexed keywords

EID: 3242698140     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.01.037     Document Type: Article

References (19)

1. Ambrosetti A. Brezis H. Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems J. Funct. Anal. 122 1994 519-543
2. Brezis H. Lieb E. A relation between pointwise convergence of functions and convergence of functionals Proc. Amer. Math. Soc. 88 1983 486-490
3. Brezis H. Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical exponents Comm. Pure Appl. Math. 34 1983 437-477
4. Barstch T. Willem M. On an elliptic equation with concave and convex nonlinearities Proc. Amer. Math. Soc. 123 1995 3555-3561
5. Caffarelli L. Gidas B. Spruck J. Asymptotic symmetry and local behaviour of semilinear elliptic equations with critical Sobolev growth Comm. Pure Appl. Math. 42 1989 271-297
6. Caffarelli L. Kohn R. Nirenberg L. First order interpolation inequalities with weights Compositio Math. 53 1984 259-275
7. Capozzi A. Fortunato D. Palmieri G. An existence result for nonlinear elliptic problems involving critical Sobolev exponent Ann. Inst. H. Poincaré Anal. Non Linéaire 2 1985 463-470
8. Chen J. Existence of solutions for a nonlinear PDE with an inverse square potential J. Differential Equations 195 2003 497-519
9. Chou K.S. Chu C.W. On the best constant for a weighted Sobolev-Hardy inequality J. London Math. Soc. 48 1993 137-151
10. Ferrero A. Gazzola F. Existence of solutions for singular critical growth semilinear elliptic equations J. Differential Equations 177 2001 494-522
11. Garcia Azorero J. Peral Alonso I. Some result about the existence of a second positive solution in a quasilinear critical problem Indiana Univ. Math. J. 43 1994 941-957
12. Garcia Azorero J. Peral Alonso I. Hardy inequalities and some critical elliptic and parabolic problems J. Differential Equations 144 1998 441-476
13. Ghoussoub N. Preiss D. A general mountain pass principle for locating and classifying critical points Ann. Inst. H. Poincaré Anal. Non Linéaire 6 1989 321-330
14. Han Q. Lin F. Elliptic partial differential equations Courant Lect. Notes Math. vol. 1 1997 Amer. Math. Soc. Providence, RI
15. Jannelli E. The role played by space dimension in elliptic critical problems J. Differential Equations 156 1999 407-426
16. D. Smets, Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities, Preprint of Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron 2, Belgium, 2001
17. Smets D. Tesei A. On a class of singular elliptic problems with first-order terms Adv. Differential Equations 8 2003 257-278
18. Terracini S. On positive entire solutions to a class of equations with singular coefficient and critical exponent Adv. Differential Equations 1 1996 241-264
19. Willem M. Minimax Theorems 1996 Birkhäuser Boston