Nonresonance impulsive functional differential inclusions with variable times

Computers and Mathematics with Applications

Volumn 47, Issue 10-11, 2004, Pages 1725-1737

  Benchohra, M ^a   Graef, J R ^b   Ouahabi, A ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

Author keywords

Condensing map; Fixed point; Impulsive functional differential inclusions; Nonresonance problem; Selection; Variable times

Indexed keywords

BOUNDARY CONDITIONS; METHOD OF MOMENTS; PROBLEM SOLVING; RESONANCE; SET THEORY; THEOREM PROVING; VARIATIONAL TECHNIQUES;

CONDENSING MAP; FIXED POINT; IMPULSIVE FUNCTIONAL DIFFERENTIAL INCLUSIONS; MARTELLI FIXED-POINT THEOREM; NONRESONANCE PROBLEM; SPACE-CRAFT CONTROL; STATE-DEPENDENT IMPULSES; VARIABLE TIMES;

DIFFERENTIAL EQUATIONS;

EID: 9644303272     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2004.06.025     Document Type: Article

References (30)

1. D.D. Bainov and P.S. Simeonov, Systems with Impulse Effect, Ellis Horwood, Chichister, (1989).
2. V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, (1989).
3. A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, (1995).
4. M. Benchohra, A. Boucherif and A. Ouahabi, On nonresonance impulsive functional differential inclusions with nonconvex valued right hand aide, J. Math. Anal. Appl. (to appear).
5. M. Benchohra, J.R. Graef, J. Henderson and S.K. Ntouyas, Nonresonance impulsive higher order functional nonconvex valued differential inclusions, Electron. J. Qual. Theory Differ. Equ. 13, 1-13, (2002).
6. M. Benchohra, J. Henderson and S.K. Ntouyas, On nonresonance impulsive functional differential inclusions with periodic boundary conditions. Intern. J. Appl. Math. 5, 377-391, (2001).
7. D. Franco, E. Liz, J.J. Nieto and Y.V. Rogovchenco, A contribution to the study of functional differential equations with impulses, Math. Nachr. 218, 49-60, (2000).
8. M. Frigon and D. O'Regan, Boundary value problems for second order impulsive differential equations using set-valued maps, Appl. Anal. 58, 325-333, (1995).
9. I. Bajo and E. Liz, Periodic boundary value problem for first order differential equations with impulses at variable times, J. Math. Anal. Appl. 204, 65-73, (1996).
10. A. Cabada, J.J. Nieto, D. Franco and S.I. Trofimchuk, A generalization of the monotone method for second order periodic boundary value problem with impulses at fixed points, Dynam. Contin. Dicrete Impuls. Systems 7, 145-185, (2000).
11. Y. Dong, Periodic boundary value problems for functional differential equations with impulses, J. Math. Anal. Appl. 210, 170-181, (1997).
12. L. Erbe and W. Krawcewicz, Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rocky Mountain J. Math. 22, 519-539, (1992).
13. M. Frigon and D. O'Regan, Impulsive differential equations with variable times, Nonlinear Anal. 26, 1913-1922, (1996).
14. M. Frigon and D. O'Regan, First order impulsive initial and periodic problems with variable moments, J. Math. Anal. Appl. 233, 730-739, (1999).
15. M. Frigon and D. O'Regan, Second order Sturm-Liouville BVP's with impulses at variable moments, Dynam. Contin. Discrete Impuls. Systems 8 (2), 149-159, (2001).
16. 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, 1263-1270, (1994).
17. S.K. Kaul and X.Z. Liu, Vector Lyapunov functions for impulsive differential systems with variable times, Dynam. Contin. Discrete Impuls. Systems 6, 25-38, (1999).
18. S.K. Kaul and X.Z. Liu, Impulsive Integra-differential equations with variable times, Nonlinear Studies 8, 21-32, (2001).
19. V. Lakshmikantham, S. Leela and S.K. Kaul, Comparison principle for impulsive differential equations with variable times and stability theory, Nonlinear Anal. 22, 499-503, (1994).
20. V. Lakshmikantham, N.B. Papageorgiou and J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments, Appl. Anal. 15, 41-58, (1993).
21. X. Liu and G. Ballinger, Existence and continuability of solutions for differential equations with delays and state-dependent impulses, Nonlinear Anal. 51, 633-647, (2002).
22. M. Benchohra and P. Eloe, On nonresonance impulsive functional differential equations with periodic boundary conditions, Appl. Math. E-Notes 1, 65-72, (2001).
23. J.J. Nieto, Basic theory for nonresonance impulsive periodic problems of first order, J. Math. Anal. Appl. 205, 423-433, (1997).
24. M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 4 (3), 70-76, (1975).
25. J. Banas and K. Goebel, Measures of Noncompactnes in Banach Spaces, Marcel-Dekker, New York, (1980).
26. K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin, (1992).
27. L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, Volume 495, Kluwer Academic, Dordrecht, (1999).
28. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, (1997).
29. A.A. Tolstonogov, Differential Inclusions in a Banach Space, Kluwer, Dordrecht, (2000).
30. 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, 781-786, (1965).