Existence and uniqueness of positive solutions for some quasilinear elliptic problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 44, Issue 2, 2001, Pages 189-204

  Drábek, Pavel ^a   Hernández, Jesús ^b  

^a UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING; VARIATIONAL TECHNIQUES;

QUASILINEAR ELLIPTIC PROBLEMS; SOBOLEV SPACES;

NONLINEAR EQUATIONS;

EID: 0342468754     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00258-8     Document Type: Article

References (22)

1. Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18:1976;620-709.
2. A. Ambrosetti, G. Prodi, A Primer of Nonlinear Analysis, Cambridge University Press, Cambridge, 1993.
3. Anane A. Simplicité et isolation de la première valeur propre du p-laplacien avec poids. C.R. Acad. Sci. Paris Sér. I Math. 305:1987;725-728.
4. s Houston, Math. J. 20:1994;99-114.
5. Brezis H., Browder F. Some properties of higher order Sobolev spaces. J. Math. Pures Appl. 61:1982;245-259.
6. Brezis H., Oswald L. Remarks on sublinear elliptic equations. Nonlinear Anal. 10:1986;55-64.
7. Brown K., Hess P. Stability and uniqueness of positive solutions for a semi-linear elliptic boundary value problem. Differential Integral Equations. 3:1990;201-207.
8. M. Cuesta, Existence results for quasilinear problems via ordered sub and supersolutions, Ann. Fac. Sciences Toulouse, in press.
9. Dancer E.N., Sweers G.S. On the existence of a maximal weak solution for a semilinear elliptic equation. Differential Integral Equations. 2:1989;533-540.
10. Deuel J., Hess P. Criterion for the existence of solutions of nonlinear elliptic boundary value problems. Proc. Roy. Soc. Edinburgh. 74A:1975;49-54.
11. J.I. Diaz, Nonlinear Partial Differential Equations and Free Boundaries, Boston, Pitman, 1985.
12. J.I. Diaz, J. Hernández, in preparation.
13. Diaz J.I., Saa J.E. Existence et unicité de solutions positives pur certaines équations elliptiques quasilinéaires. Comptes Rendus Acad. Sci. Paris. 305:1987;521-524.
14. P. Drábek, A. Kufner, F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter Series in Nonlinear Analysis and Applications, Vol. 5, Berlin, New York, 1997.
15. J. Fleckinger, J. Hernández, P. Takáč, F. de Thélin, Uniqueness and positivity for solutions of equations with the p -Laplacian, in: G. Caristi, E. Mitidieri (Eds.), Reaction Diffusion Systems, Marcel Dekker, New York, 1998, pp. 141-155.
16. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, Heidelberg, New York, 1977.
17. J. Hernández, Positive solutions for the logistic equations with unbounded weights, in: G. Caristi, E. Mitidieri (Eds.), Reaction Diffusion Systems, Marcel Dekker, New York, 1998, pp. 183-197.
18. J. Hernández, F. Mancelo, J.M. Vega de Prada, On the linearization of some singular nonlinear elliptic problems and applications, in preparation.
19. M. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, London, 1964.
20. p-2 u = 0 Proc. Amer. Math. Soc. 109:1990;157-164.
21. J.L. Lions, E. Magenes, Problémes aux Limites non Homogènes et Applications, Vol.1, Dunod, Paris, 1968.
22. Vázquez J.L. A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12:1984;191-202.