Perturbed functional and neutral functional evolution equations with infinite delay in fréchet spaces

Electronic Journal of Differential Equations

Volumn 2008, Issue , 2008, Pages 1-19

  Baghli, Selma ^a   Benchohra, Mouffak ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Fixed point theory; Fr chet spaces; Infinite delay; Mild solution; Neutral evolution equations; Nonlinear alternative; Perturbed functional equation

Indexed keywords

EID: 44349111167     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. M. Adimy, H. Bouzahir and K. Ezzinbi; Existence for a class of partial functional differential equations with infinite delay, Nonlinear Anal., 46 (2001), 91-112.
2. M. Adimy, H. Bouzahir and K. Ezzinbi; Local existence and stability for some partial functional differential equations with infinite delay, Nonlinear Anal., 48 (2002), 323-348.
3. M. Adimy, H. Bouzahir and K. Ezzinbi; Existence and stability for some partial neutral functional differential equations with infinite delay, J. Math. Anal. Appl., 294 (2004), 438-461.
4. N. U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, 246. Longman Scientific & Technical, Harlow John Wiley & Sons, Inc., New York, 1991.
5. N. U. Ahmed, Dynamic Systems and Control with Applications, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.
6. A. Arara, M. Benchohra, L. Górniewicz and A. Ouahab; Controllability results for semilinear functional differential inclusions with unbounded delay, Math. Bulletin. 3 (2006), 157-183.
7. C. Avramescu, Some remarks on a fixed point theorem of Krasnoselskii, Electronic J. Qual. The. Diff. Equa., 5 (2003), 1-15.
8. S. Baghli and M. Benchohra; Uniqueness results for partial functional differential equations in Fréchet spaces, Fixed Point Theory (to appear).
9. S. Baghli and M. Benchohra; Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces, Georgian Math. J. (to appear).
10. K. Balachandran and E. R. Anandhi; Controllability of neutral functional integrodifferential infinite delay systems in Banach spaces, Taiwanese J. Math., 8 (2004), 689-702.
11. K. Balachandran and A. Leelamani; Null controllability of neutral integrodifferential systems with infinite delay, Math. Problems Engineering, 2006 (2006), 1-18.
12. M. Belmekki, M. Benchohra, K. Ezzinbi and S. K. Ntouyas; Existence results for some partial functional differential equations with infinite delay, Nonlinear Stud. (to appear).
13. M. Belmekki, M. Benchohra and S. K. Ntouyas; Existence results for semilinear perturbed functional differential equations with nondensely defined operators, Fixed Point Th. Appl., 2006, (2006), 1-13.
14. M. Belmekki, M. Benchohra and S. K. Ntouyas; Existence results for densely defined semi-linear functional differential inclusions, J. Contemporary Math., 1 (1) (2008), 25-44.
15. M. Belmekki, M. Benchohra and S. K. Ntouyas; Existence results for nondensely defined semi-linear functional differential inclusions, J. Nonlinear Func. Anal. Differ. Equ 1 (2) (2007), 261-279.
16. M. Benchohra and L. Gorniewicz; Existence results of nondensely defined impulsive semilinear functional differential inclusions with infinite delay, J. Fixed Point Th. Appl., 2 (1) (2007), 11-51.
17. M. Benchohra, L. Górniewicz and S. K. Ntouyas; Controllability of Some Nonlinear Systems in Banach spaces : The fixed point theory approach, Pawel Wlodkowicz University College, Plock, 2003.
18. M. Benchohra and S. K. Ntouyas; Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition, Comment. Math. Univ. Carolinae, 41 (3) (2000), 485-491.
19. T. A. Burton, A fixed-point theorem of Krasnoselskii; Appl. Math. Letters, 11 (1) (1998), 85-88.
20. T. A. Burton and C. Kirk; A fixed point theorem of Krasnoselskii type, Math. Nachrichten, 189 (1998), 23-31.
21. C. Corduneanu and V. Lakshmikantham; Equations with unbounded delay, Nonlinear Anal., 4 (1980), 831-877.
22. K.J. Engel and R. Nagel; One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000.
23. K. Ezzinbi; Existence and stability for some partial functional differential equations with infinite delay, Electronic J. Diff Equa., 2003 (116) (2003), 1-13.
24. A. Freidman; Partial Differential Equations, Holt, Rinehat and Winston, New York, 1969.
25. J. Hale and J. Kato; Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.
26. J. K. Hale and S. M. Verduyn Lunel; Introduction to Functional Differential Equations, Applied Mathematical Sciences 99, Springer-Verlag, New York, 1993.
27. S. Heikkila and V. Lakshmikantham; Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations, Marcel Dekker Inc., New York, 1994.
28. H. R. Henriquez; Existence of periodic solutions of neutral functional differential equations with unbounded delay, Proyecciones, 19 (3) (2000), 305-329.
29. E. Hernandez; Regularity of solutions of partial neutral functional differential equations with unbounded delay, Proyecciones, 21 (1) (2002), 65-95.
30. E. Hernandez; A Massera type criterion for a partial neutral functional differential equation, Electronic J. Differ. Equa., 2002 (40) (2002), 1-17.
31. Y. Hino and S. Murakami; Total stability in abstract functional differential equations with infinite delay, Electronic J. of Qualitative Theory of Diff. Equa., Lecture Notes in Mathematics, 1473, Springer-Verlag, Berlin, 1991.
32. Y. Hino, S. Murakami, and T. Naito; Functional Differential Equations with Unbounded Delay, Lecture Notes in Mathematics, 1473, Springer-Verlag, Berlin, 1991.
33. F. Kappel and W. Schappacher; Some considerations to the fundamental theory of infinite delay equations, J. Differential Equations, 37 (1980), 141-183.
34. V. Kolmanovskii, and A. Myshkis; Introduction to the Theory and Applications of Functional-Differential Equations. Mathematics and its Applications, 463. Kluwer Academic Publishers, Dordrecht, 1999.
35. A. Pazy; Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
36. K. Schumacher; Existence and continuous dependence for differential equations with unbounded delay, Arch. Rational Mech. Anal., 64 (1978), 315-335.
37. J. Wu; Theory and Applications of Partial Functional Differential Equations, Applied Mathematical Sciences 119, Springer-Verlag, New York, 1996.
38. K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin, 1980.