The nehari manifold for systems of nonlinear elliptic equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 10, 2006, Pages 2149-2167

  Adriouch, K ^a   El Hamidi, A ^a  

^a UNIVERSITÉ DE LA ROCHELLE   (France)

Author keywords

(p,q) Laplacian; Ekeland's principle; Nehari manifold; Palais Smale

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES;

(P,Q)-LAPLACIAN; CONVEX NONLINEARITIES; DIRICHLET; EKELAND'S PRINCIPLE; MIXED BOUNDARY CONDITIONS; MULTIPLICITY RESULTS; NEHARI MANIFOLD; PALAIS-SMALE;

NONLINEAR EQUATIONS;

EID: 33644921520     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.06.003     Document Type: Article

References (24)

1. A. Ahammou Positive radial solutions of nonlinear elliptic systems New York J. Math. 7 2001 267 280
2. C.O. Alves, and D.G. de Figueiredo Nonvariational elliptic systems, Current developments in partial differential equations (Temuco, 1999) Discrete Contin. Dyn. Systems 8 2 2002 289 302
3. C.O. Alves, D.C. de Morais Filho, and M.A.S. Souto On systems of elliptic equations involving subcritical or critical Sobolev exponents Nonlinear Anal. T. M. A. 42 5 2000 771 787
4. A. Ambrosetti, H. Brézis, and G. Cerami Combined effects of concave and convex nonlinearities in some elliptic problems J. Funct. Anal. 122 2 1994 519 543
5. A. Ambrosetti, J. Garcia Azorero, and I. Peral Existence and multiplicity results for some nonlinear elliptic equations: a survey Rend. Mat. Appl. 20 7 2000 167 198
6. Y. Bozhkov, and E. Mitidieri Existence of multiple solutions for quasilinear systems via fibering method J. Differential Equations 190 1 2003 239 267
7. K.J. Brown, and Y. Zhang The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function J. Differential Equations 193 2 2003 481 499
8. P. Clément, D.G. de Figueiredo, and E. Mitidieri Positive solutions of semilinear elliptic systems Commun. Partial Differential Equations 17 5-6 1992 923 940
9. E. Colorado, and I. Peral Semilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions J. Funct. Anal. 199 2 2003 468 507
10. D.G. de Figueiredo Nonlinear elliptic systems An. Acad. Brasil. Ciênc. 72 4 2000 453 469
11. D.G. de Figueiredo, and P. Felmer On superquadratic elliptic systems Trans. Amer. Math. Soc. 343 1 1994 99 116
12. P. Drabek, and S. Pohozaev Positive solutions for the p-Laplacian: application of the fibering method Proc. Roy. Soc. Edinburgh Sect. A 127 1997 703 726
13. I. Ekeland On the variational principle J. Math. Anal. Appl. 47 1974 324 353
14. A. El Hamidi Multiple solutions with changing sign energy to a nonlinear elliptic equation Commun. Pure Appl. Anal. 3 2 2004 253 265
15. A. El Hamidi Existence results to elliptic systems with nonstandard growth conditions J. Math. Anal. Appl. 300 1 2004 30 42
16. J. Mawhin, and M. Willem Critical Point Theory and Hamilton Systems 1989 Springer Berlin
17. Z. Nehari On a class of nonlinear second-order differential equations Trans. Amer. Math. Soc. 95 1960 101 123
18. P.H. Rabinowitz Minimax methods in critical point theory with applications to differential equations Reg. Conf. Ser. Math. 65 1986 1 100
19. M. Squassina An eigenvalue problem for elliptic systems New York J. Math. 6 2000 95 106
20. M. Struwe Variational methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems 1996 Springer Berlin
21. G. Tarantello On nonhomogeneous elliptic equations involving critical Sobolev exponent Ann. Inst. H. Poincarè Anal. Non Linèaire 9 3 1992 281 304
22. J. Vélin Existence results for some nonlinear elliptic system with lack of compactness Nonlinear Anal. 52 3 2003 1017 1034
23. J. Vélin, and F. de Thélin Existence and nonexistence of nontrivial solutions for some nonlinear elliptic systems Rev. Mat. Univ. Complut. Madrid 6 1 1993 153 194
24. M. Willem Minimax theorems Progress in Nonlinear Differential Equations and their Applications vol. 24 1996 Birkhäuser Boston, Inc. Boston, MA