On some nonlinear elliptic systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 59, Issue 5, 2004, Pages 695-706

  Djellit, Ali ^a   Tas, Saâdia ^a  

^a BADJI MOKHTAR UNIVERSITY   (Algeria)

Author keywords

Fixed point theorem; Nonlinear elliptic system; p Laplacian; Radial solution

Indexed keywords

FUNCTIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

FIXED POINT THEOREM; NONLINEAR ELLIPTIC SYSTEM; P-LAPLACIAN OPERATOR; RADIAL SOLUTION;

NONLINEAR SYSTEMS;

EID: 7044226026     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.07.029     Document Type: Article

References (19)

1. C. Atkinson, C.R. Champion, On some boundary value problems for the equation ∇ ·(F|∇ω|)∇ω = 0, Proc. Roy. Soc. London Ser. A 448 (1995) 269-279.
2. C. Atkinson, K. El-Ali, Some boundary value problems for the Bingham model, J. Non-Newtonian Fluid Mech. 41 (1992) 339-363.
3. T.B. Benjamin, A unified theory of conjugate flows, Philos. Trans. Roy. Soc. 269A (1971) 587-643.
4. L. Boccardo, D.G. de Figueiredo, Some remarks on a system of quasilinear elliptic equations, Nonlinear Differential Equations Appl. 9 (2002) 309-323.
5. Ph. Clément, D.G. de Figueiredo, E. Mitidieri, Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations 17 (5, 6) (1992) 923-940.
6. Ph. Clément, J. Fleckinger, E. Mitidieri, F. de Thélin, Existence of positive solutions for a nonvariational quasilinear elliptic systems, J. Differential Equations 166 (2000) 455-477.
7. Ph. Clément, R. Manasevich, E. Mitidieri, Positive solutions for a quasilinear system via Blow up, Comm. Partial Differential Equations 18 (12) (1993) 2071-2106.
8. N, Eur. J. Differential Equations 1994 (07) (1994) 1-14.
9. D.G. 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.
10. N involving the p-Laplacian, Eur. J. Differential Equations 2003 (56) (2003) 1-8.
11. N, Eur. J. Differential Equations 1997 (11) (1997) 1-15.
12. B. Gidas, J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 6 (8) (1981) 883-901.
13. M.A. Krasnosel'skii, Fixed points of cone-compressing and cone-extending operators, Soviet Math. Dokl. 1 (1960) 1285-1288.
14. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, Paris, 1969.
15. P.M. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992) 270-291.
16. D.R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, 1974.
17. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984) 126-150.
18. L.S. Yu, Nonlinear p-Laplacian problems on unbounded domains, Proc. Amer. Math. Soc. 115 (4) (1992) 1037-1045.
19. E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II/ B Nonlinear Monotone Operators, vol. III Variational Methods and Optimization, Springer, Berlin, 1990.