Existence of a periodic solution for some partial functional differential equations with infinite delay

Journal of Mathematical Analysis and Applications

Volumn 256, Issue 1, 2001, Pages 257-280

  Benkhalti, Rachid ^a   Bouzahir, Hassane ^b   Ezzinbi, Khalil ^b  

^a PACIFIC LUTHERAN UNIVERSITY   (United States)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035315101     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7321     Document Type: Article

References (25)

1. M. Adimy, H. Bouzahir, and, K. Ezzinbi, Existence for a class of partial functional differential equations with infinite delay, J. Nonlinear Anal, in press.
2. M. Adimy, H. Bouzahir, and, K. Ezzinbi, Local existence and stability for a class of partial functional differential equations with infinite delay, J. Nonlinear Anal, in press.
3. Adimy M., Ezzinbi K. Local existence and linearized stability for partial functional differential equations. Dynam. Systems Appl. 7:1998;389-404.
4. Bouzahir H., Ezzinbi K. Global attractor for a class of partial functional differential equations with infinite delay. Freitas P., Faria T. Topics in Functional Differential and Difference Equations. Fields Inst. Commun. 20:2000;Amer. Math. Soc. Providence.
5. Busenberg S., Wu B. Convergence theorems for integrated semigroups. Differential Integral Equations. 1992;509-520.
6. Chow S. N., Hale J. K. Strongly limit-compact maps. Funkcial. Ekvac. 17:1974;31-38.
7. Da Prato G., Sinestrari E. Differential operators with non-dense domains. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14:1987;285-344.
8. Hale J. K., Kato J. Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21:1978;11-41.
9. Henriquez H. R. Periodic solutions of quasi-linear partial functional differential equations with unbounded delay. Funkcial. Ekvac. 37:1994;329-343.
10. Henriquez H. R. Approximation of abstract functional differential equations with unbounded delay. Indian J. Pure Appl. Math. 27:1996;357-386.
11. Henriquez H. R. Regularity of solutions of abstract retarded functional differential equations with unbounded delay. Nonlinear Anal. 28:1997;513-531.
12. Hino Y., Murakami S., Naito T. Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics. 1473:1991;Springer-Verlag, Berlin.
13. Hino Y., Murakami S., Yoshizawa T. Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space. Tôhoku Math. J. 49:1997;133-147.
14. Kellermann H., Hieber H. Integrated semigroup. J. Funct. Anal. 15:1989;160-180.
15. S. Murakami, Stability for functional differential equations with infinite delay in Banach space, preprint.
16. Nussbaum R. D. The radius of essential spectrum. Duke Math. J. 37:1970;473-478.
17. Sadovskii B. N. On a fixed point principle. Funct. Anal. Appl. 1:1967;74-76.
18. Shin J. S. Comparison theorems and uniqueness of mild solutions to semilinear functional differential equations in Banach spaces. Nonlinear Anal. 23:1994;825-847.
19. Shin J. S. An existence theorem of a functional differential equation. Funkcial. Ekvac. 30:1987;19-29.
20. Shin J. S., Naito T. Semi-Fredholm operators and periodic solutions for linear functional differential equations. J. Differential Equations. 153:1999;407-441.
21. Thieme H. Semiflows generated by Lipschitz perturbations of non-densely defined operators. Differential Integral Equations. 3:1990;1035-1066.
22. Travis C. C., Webb G. F. Existence and stability for partial functional differential equations. Trans. Amer. Math. Soc. 200:1974;395-418.
23. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1992;Springer-Verlag, New York.
24. Webb G. F. Theory of Nonlinear Age-Dependent Population Dynamics. 1985;Dekker, New York.
25. Wu J. Theory and Applications of Partial Functional Differential Equations. 1996;Springer-Verlag, New York/Berlin.