Liouville theorems for elliptic inequalities and applications

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 6, 1998, Pages 1217-1247

  Birindelli, Isabeau ^a   Mitidieri, Enzo ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF TRIESTE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747078140     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500027293     Document Type: Article

References (18)

1. S. Agmon, A. Douglis and L. Nirenberg. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Comm. Pure Appl. Math. 12 (1959), 623-727.
2. H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg. Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires. C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 945-50.
3. H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg. Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Topol. Methods Nonlinear Anal. 4 (1995), 59-78.
4. H. Berestycki, L. Nirenberg and S. R. S. Varadhan. The principal eigenvalue and maximum principle for second order elliptic operator in general domains. Comm. Pure Appl. Math. 47 (1994), 47-92.
5. G. Caristi and E. Mitidieri. Non existence of positive solutions for quasilinear equations. Adv. Differential Equations 2 (1997), 319-59.
6. Ph. Clément, D. G. de Figueiredo and E. Mitidieri. A priori estimates for positive solutions of semilinear elliptic systems via Hardy-Sobolev inequalities. In Nonlinear Partial Differential Equations, Pitman Research Notes in Mathematics 343, 3-91 (Harlow: Longman, 1996).
7. Ph. Clément, R. Manasevich and E. Mitidieri. Positive solutions for a quasilinear system via blow up. Comm. Partial Differential Equations 18 (1993), 2071-106.
8. E. N. Dancer. Some notes on the method of moving planes. Bull. Austral. Math. Soc. 46 (1992), 425-34.
9. D. G. de Figueiredo and P. Felmer. A Liouville-type theorem for elliptic systems. Ann. Scuola Norm. Cl. Sci. (4) (1992), 387-97.
10. B. Gidas and J. Spruck. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 35 (1981), 525-98.
11. B. Gidas and J. Spruck. A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Partial Differential Equations 6 (1981), 883-901.
12. D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order (Berlin: Springer, 1983).
13. n. Differential Integral Equations 9 (1996), 465-79.
14. M. Nicolescu. Les fonctions polyharmoniques (Paris: Herman, 1936).
15. J. Serrin and H. Zou. Non-existence of positive solutions of Lane-Emden systems. Differential Integral Equations 9 (1996), 635-53.
16. M. A. S. Souto. A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems. Differential Integral Equations 8 (1995), 1245-58.
17. G. Sweers. Personal communication (1996).
18. F. Treves. Basic Linear Partial Differential Equations (New York: Academic Press, 1975).