Structure of Solutions Sets and a Continuous Version of Filippov's Theorem for First Order Impulsive Differential Inclusions with Periodic Conditions

Electronic Journal of Qualitative Theory of Differential Equations

Volumn , Issue , 2009, Pages 1-23

  Graef, John R ^a   Ouahab, Abdelghani ^b  

^a UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

^b UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Acyclic; Continuous selection; Contractible; Filippov's theorem; Impulsive differential inclusions; Periodic conditions; R set

Indexed keywords

EID: 67649556632     PISSN: None     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2009.1.24     Document Type: Article

References (43)

1. Z. Agur, L. Cojocaru, G. Mazaur, R. M. Anderson, and Y. L. Danon, Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci. USA. 90 (1993), 11698-11702.
2. J. Andres, G. Gabor, and L. Górniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861-4903.
3. J. Andres, G. Gabor, and L. Górniewicz, Topological structure of solution sets to multivalued asymptotic problems, Z. Anal. Anwendungen 18, (1999), 1-20.
4. J. Andres, G. Gabor, and L. Górniewicz, Acyclicity of solutions sets to functional inclusions, Nonlinear Anal, 49 (2002), 671-688.
5. N. Aronszajn, Le correspondant topologique de l'unicité dans la théorie des équations différentielles, Ann. Math. 43 (1942), 730-738.
6. J. P. Aubin, Impulse differential inclusions and hybrid systems: a viability approach, Lecture Notes, Université Paris-Dauphine, 2002.
7. J. P. Aubin, and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, New York, 1984.
8. J. P. Aubin, and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990.
9. D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect, Ellis Horwood Ltd., Chichister, 1989.
10. M. Benchohra, A. Boucherif, and A. Ouahab, On nonresonance impulsive functional differential inclusions with nonconvex valued right hand side, J. Math. Anal. Appl., 282 (2003), 85-94.
11. M. Benchohra, J. Henderson, and S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Contemporay Mathematics and Its Applications, Hindawi Publishing, New York, 2006.
12. n, Dynamics Reported: Expositions in Dynamical Systems (N.S.) 1 (1992), 225-250.
13. A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 70-85.
14. F. E. Browder and G. P. Gupta, Topological degree and nonlinear mappings of analytic type in Banach spaces, J. Math. Anal. Appl., 26, (1969), 730-738.
15. C. Castaing, and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
16. R. M. Colombo, A. Fryszkowski, T. Rzeẑuchowski, and V. Staticu, Continuous selection of solution sets of Lipschitzean differential inclusions, Funkcial. Ekvac. 34 (1991), 321-330.
17. K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin-New York, 1992.
18. S. Djebali, L. Górniewicz, and A. Ouahab, Filippov's theorem and solution sets for first order impulsive semilinear functional differential inclusions, Topol. Meth. Nonlin. Anal., 32, (2008), 261-312.
19. M. Frigon and A. Granas, Théoremes d'existence pour des inclusions différentielles sans convexité, C. R. Acad. Sci. Paris, Ser. I 310 (1990), 819-822.
20. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and Its Applications, 495, Kluwer, Dordrecht, 1999.
21. L. Górniewicz, On the solution sets of differential inclusions, J. Math. Anal. Appl. 113 (1986) 235-244.
22. L. Górniewicz, Homological methods in fixed point theory of multivalued maps, Dissertations Math. 129 (1976), 1-71.
23. L. Górniewicz, Topological structure of solutions sets: current results, CDDE 2000 Proceedings (Brno), Arch. Math. (Brno) 36 (2000), suppl., 343-382.
24. L. Górniewicz, P. Nistri, and V. Obukhovskii, Differential inclusions on proximate retracts of Hilbert spaces, Int. J. Nonlinear Diff. Equs., TMA 3 (1995), 13-26.
25. J. R. Graef and A. Ouahab, Nonresonance impulsive functional dynamic boundary value inclusions on time scales, Nonlinear Studies, 15 (2008), 339-354.
26. J. R. Graef and A. Ouahab, Nonresonance impulsive functional dynamic equations on times scales, Int. J. Appl. Math. Sci. 2 (2005), 65-80.
27. J. R. Graef and A. Ouahab, First order impulsive differential inclusions with periodic condition, Electron. J. Qual. Theory Differ. Equ. 31 (2008), 1-40.
28. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
29. G. Haddad and J. M. Lasry, Periodic solutions of functional differential inclusions and fixed points of σ-selectionable correspondences, J. Math. Anal. Appl. 96 (1983), 295-312.
30. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, 1997.
31. D. M. Hyman, On decreasing sequences of compact absolute retracts, Fund. Math. 64 (1969) 91-97.
32. M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multi-valued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter, Berlin, 2001.
33. M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
34. E. Kruger-Thiemr, Formal theory of drug dosage regiments. I. J. Theoret. Biol., 13 (1966), 212-235.
35. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
36. J. M. Lasry and R. Robert, Analyse non linéaire multivoaque. Cahier de Math de la déicision No. 761 I. Université de Paris-Dauphine.
37. A. Ouahab, Some Contributions in Impulsive Differential Equations and Inclusions with Fixed and Variable Times, Ph.D. Dissertation, University of Sidi-Bel-Abbès (Algeria), 2006.
38. S. G. Pandit and S. G. Deo, Differential Systems Involving Impulses, Lecture Notes in Mathematics Vol 954, Springer-Verlag, 1982.
39. G. Peano, Démonstration de l'integrabilite des équations differentielles ordinaires, Mat. Annalen 37 (1890), 182-238.
40. G. Peano, Sull'integrabilità delle equazioni differenziali del primo ordine, Atti. della Reale Accad. dell Scienze di Torino 21 (1886), 677-685.
41. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
42. A. A. Tolstonogov, Differential Inclusions in a Banach Space, Kluwer, Dordrecht, 2000.
43. Q. J. Zhu, On the solution set of differential inclusions in Banach Space, J. Differential Equations 93 (1991), 213-237.