A priori estimates and existence of positive solutions for strongly nonlinear problems

Journal of Differential Equations

Volumn 199, Issue 1, 2004, Pages 96-114

  Ruiz, D ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

A priori estimates; Blow up; Harnack inequalities; m Laplacian

Indexed keywords

EID: 1842784084     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2003.10.021     Document Type: Article

References (25)

1. W. Allegretto, Y.X. Huang, A Picone's identity for the p-Laplacian and applications, Nonlinear Anal. 32 (7) (1998) 819-830.
2. A. Ambrosetti, G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat Pura Appl. 4 (93) (1972) 231-246.
3. D. Arcoya, J.L. Gámez, Bifurcation theory and related problems: anti-maximum principle and resonance, Comm. Partial Differential Equations 26 (2001) 1879-1911.
4. C. Azizieh, P. Clément, A priori estimates and continuation methods for positive solutions of p-laplace equations, J. Diff. Eq. 179 (2002) 213-245.
5. H. Brezis, R.E.L. Turner, On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614.
6. L. Damascelli, F. Pascella, Monotonicity and symmetry of solutions of p-Laplace equations, 1 < p < 2, via the moving plane method, Ann. Scuola. Norm. Pisa, Cl. Sci. 26 (4) (1998) 689-707.
7. E.N. Dancer, Fixed point index calculations and applications, in: M. Maetzu, A. Vignoli (Eds.), Topological Nonlinear Analysis; Degree, Singularity and Variations, Birkhauser, Boston, 1995, pp. 303-340.
8. D. de Figueiredo, P.L. Lions, R.D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl. 61 (1982) 41-63.
9. D. de Figueiredo, J. Yang, A priori bounds for positive solutions of a non-variational elliptic system, Comm. Partial Differential Equations 26 (2001) 2305-2321.
10. 1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983) 827-850.
11. B. Gidas, J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525-598.
12. B. Gidas, J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 6 (1981) 883-901.
13. M.A. Krasnoselskii, Fixed point of cone-compressing or cone-extending operators, Soviet. Math. Dokl. 1 (1960) 1285-1288.
14. G.M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988) 1203-1219.
15. E. Mitidieri, S.I. Pohozaev, The absence of global positive solutions to quasilinear elliptic inequalities, Dokl. Math. 57 (1998) 250-253;
16. E. Mitidieri, S.I. Pohozaev, The absence of global positive solutions to quasilinear elliptic inequalities, Dokl. Akad. Nauk. 359 (1998) 456-460.
17. M. Montenegro, M. Montenegro, Existence and nonexistence of solutions for quasilinear elliptic equations, J. Math. Anal. Appl. 245 (2000) 303-316.
18. P.H. Rabinowitz, Some aspects of nonlinear eigenvalue problems, Rocky Mountain J. Math. 3 (1973) 161-202.
19. J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math. 111 (1964) 247-302.
20. J. Serrin, H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities, Acta Math. 189 (2002) 79-142.
21. J. Simon, Régularité de la solution d'un problème aux limites non linèaires, Ann. Fac. Sc. Toulouse Math. 3 (6) (1981) 247-274.
22. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Diff. Eq. 51 (1984) 126-150.
23. N. Trudinger, On Harnack type inequalities and their applications to quasilinear elliptic equations, Comm. Pure Appl. Math. 20 (1967) 721-747.
24. J.L. Vázquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. 12 (1984) 191-202.
25. X.J. Wang, Y.-B. Deng, Existence of multiple solutions to nonlinear elliptic equations of nondivergence form, J. Math. Anal. Appl. 189 (1995) 617-630.