A priori estimates for a semilinear elliptic system without variational structure and their applications

Mathematische Annalen

Volumn 323, Issue 4, 2002, Pages 713-735

  Zou, Henghui ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035982241     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080200324     Document Type: Article

References (24)

1. Birindelli, I., Mitidieri, E., Liouville theorems for elliptic inequalities and applications. Proc. Royal Society Edinburg 128 (1998), 1217-1247
2. Brezis, H., Turner, R., On a class of superlinear elliptic equations. Comm. PDE. 2 (1977), 601-614
3. Clement, Ph., de Figueiredo, D.G., Mitidieri, E., Positive solutions of semilinear elliptic systems. Comm. PDE. 17 (1992), 923-940
4. Cosner, C., Positive solutions for superlinear elliptic systems without variational structure. Nonlinear Analysis 8 (1984), 1427-1436
5. Dancer, E.N., Some notes on the method of moving planes. Bull. Austral. Math. Soc. 46 (1992), 425-434
6. de Figueiredo, D., Semilinear elliptic systems. Nonlinear Funct. Anal. Appl. Diff. Equ., World Sci. Publishing, River Edge, NJ, 1998, pp. 122-152
7. de Figueiredo, D., Felmer, P., A Liouville type theorem for systems. Annali Scuola Norm. Sup. Pisa 21 (1994), 387-397
8. de Figueiredo, D., Lions, P., Naussbaum, R., A priori estimates and existence of positive solutions of semilinear elliptic equations. J. Math. Pures et Appl. 61 (1982) 41-63
9. Fowler, R. H., Further studies of Emden's and similar differential equations. Quart. J. Math., Oxford Ser. 2 (1931) 259-288
10. Gidas, B., Spruck. J., Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 34 (1981), 525-598
11. Gidas, B., Spruck, J., A priori bounds for positive solutions of nonlinear elliptic equations. Comm. in PDE. 6 (1981), 883-901
12. Gilbarg, D., Trudinger, N.S., Elliptic partial differential equations of second order. Springer-Verlag, New York, 1983 (second-edition)
13. Krasnosel'skii, M.A., Fixed points of cone-compressing and cone-extending operators. Soviet. Math. Dolk. 1 (1960), 1285-1288
14. Mitidieri, E., A Rellich type identity and applications. Comm. PDE 18 (1993), 125-151
15. n. Diff. Int. Equations 9 (1996), 456-479
16. Peletier, L.A., van der Vorst, R.C.A.M., Exiatence and non-existence of positive solutions of nonlinear elliptic systems and the biharmonic equations. Diff. Int. Equations 5 (1992), 747-767
17. Pohozaev, S.I., Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl. 6 (1965), 1408-1411 (English translation, Dokl. Akad. Nank. SSRR 165 (1965), 33-36)
18. Protter, M., Weinberger, H., Maximum principles in differential equations. Springer-Verlag, New York, 1984
19. Rabinowitz, P. H., Minimax mehtods in critical point theory with applications to differential equations, Regional Conf. math., no. 65, 1986
20. Reichel W., Zou, H., Non-existence results for semilinear cooperative elliptic systems via moving spheres, J. Differential Eqs., 161 (2000), 219-243
21. Serrin, J., Zou, H., Non-existence of positive solutions of the Lane-Emden system. Differential Integral Eqs. 9 (1996), 635-653
22. Serrin, J., Zou, H., Existence of entire positive solutions of elliptic Hamiltonian systems. Comm. in PDE 23 (1998), 577-599
23. van der Vorst, R.C.A.M., Variational identities and applications to differential systems. Arch. Rational Mech. Anal. 116 (1991), 375-398
24. p = 0. Annali Scuola Norm. Sup. Pisa 3 (1994), 343-356