Upper and lower solutions method for impulsive differential inclusions with nonlinear boundary conditions and variable times

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 12, Issue 3-4, 2005, Pages 383-396

  Benchohra, M ^a   Graef, J R ^b   Ntouyas, S K ^c   Ouahab, A ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

^c UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Boundary value problem; Convex multi valued map; Fixed point; Impulsive differential inclusions; Nonlinear boundary value problem; Upper and lower solutions; Variable times

Indexed keywords

EID: 18444415174     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. I. Bajo and E. Liz, Periodic boundary value problem for first order differential equations with impulses at variable times, J. Math. Anal. Appl. 204 (1996), 65-73.
2. M. Benchohra and A. Boucherif, Initial value problems for impulsive differential inclusions of first order, Differential Equations Dynam. Systems 8 (2000), 51-66.
3. M. Benchohra and S. K. Ntouyas, The lower and upper solutions method for first order differential inclusions with nonlinear boundary conditions, J. Inequal. Pure Appl. Math. 3 (2002) (1) Art. 14, 8 pp.
4. M. Benchohra, J. Henderson, and S. K. Ntouyas, On first order impulsive differential inclusions with periodic boundary conditions, Dynam. Contin. Discrete Impuls. Systems 9 (3) (2002), 417-428.
5. M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahabi, Upper and lower solutions method for first order impulsive differential inclusions with nonlinear boundary conditions, Comput. Math. Appl., to appear.
6. A. Cabada and E. Liz, Discontinuous impulsive differential equations with nonlinear boundary conditions, Nonlinear Anal. 28 (1997), 1491-1499.
7. K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992.
8. J. Dugundji and A. Granas, Fixed Point Theory, Mongrafie Mat. PWN, Warsaw, 1982.
9. M. Frigon and D. O'Regan, Existence results for first order impulsive differential equations, J. Math. Anal. Appl. 193 (1995), 96-113.
10. M. Frigon and D. O'Regan, Impulsive differential equations with variable times, Nonlinear Anal. 26 (1996), 1913-1922.
11. M. Frigon and D. O'Regan, First order impulsive initial and periodic problems with variable moments, J. Math. Anal. Appl. 233 (1999), 730-739.
12. L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and Its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
13. S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, 1994.
14. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997.
15. S. K. Kaul, V. Lakshmikantham, and S. Leela, Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times, Nonlinear Anal. 22 (1994), 1263-1270.
16. S. K. Kaul and X. Z. Liu, Impulsive integro-differential equations with variable times, Nonlinear Studies 8 (2001), 21-32.
17. V. Lakshmikantham, S. Leela and S. K. Kaul, Comparison principle for impulsive differential equations with variable times and stability theory, Nonlinear Anal. 22 (1994), 499-503.
18. V. Lakshmikantham, N. S. Papageorgiou, and J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments, Appl. Anal. 15 (1993), 41-58.
19. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
20. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
21. X. Liu, Nonlinear boundary value problems for first order impulsive differential equations, Appl. Anal. 36 (1990) 119-130.
22. E. Liz, Abstract monotone iterative techniques and applications to impulsive differential equations, Dynam. Contin. Discrete Impulsive Systems 3 (1997), 443-452.
23. E. Liz, Existence and approximation of solutions for impulsive differential equations with nonlinear boundary conditions, Nonlinear Anal. 25 (1995), 1191-1198.
24. A. M. Samoilenko, and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.