Mild solutions for impulsive neutral functional differential equations with state-dependent delay

Semigroup Forum

Volumn 80, Issue 3, 2010, Pages 375-390

  Cuevas, Claudio ^a   N'Guérékata, Gaston M ^b   Rabelo, Marcos ^a  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b MORGAN STATE UNIVERSITY   (United States)

Author keywords

Evolution family of operators; Impulsive neutral functional differential equations; Mild solutions; State dependent delay

Indexed keywords

EID: 77952420652     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-010-9213-6     Document Type: Article

References (33)

1. Agarwal, R., Diagana, T., Hernández, E.: Weighted pseudo almost periodic solutions to some partial neutral functional differential equations. J. Nonlinear Convex Anal. 8(3), 397-415 (2007).
2. Aiello, W., Freedman, H., Wu, J.: Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52(3), 855-869 (1992).
3. Alexander, V., Rezounenko, A.: Partial differential equations with discrete and distributed state-dependent delays. J. Math. Anal. Appl. 326(2), 1031-1045 (2007).
4. Anguraj, A., Arjunan, A., Mallika, M., Hernández, E.: Existence results for an impulsive neutral functional differential equation with state-dependent delay. Appl. Anal. 86(7), 861-872 (2007).
5. Baghli, S., Benchohra, M.: Perturbed functional and neutral functional evolution equations with infinite delay in Fréchet spaces. Electron. J. Differ. Equ. 69, 1-19 (2008).
6. Cao, Y., Fan, J., Gard, T.: The effects of state-dependent time delay on a stage-structured population growth model. Nonlinear Anal. TMA 19(2), 95-105 (1992).
7. Chen, F., Sun, D., Shi, J.: Periodicity in a food-limited population model with toxicants and state dependent delays. J. Math. Anal. Appl. 288(1), 136-146 (2003).
8. Cuevas, C., Hernández, E., Rabelo, M.: The existence of solutions for impulsive neutral functional differential equations. Comput. Math. Appl. 58(4), 744-757 (2009).
9. Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003).
10. Hale, J., Kato, J.: Phase space for retarded equations with infinite delay. Funkc. Ekvacioj. 21(1), 11-41 (1978).
11. Hale, J., Verduyn Lunel, S.: Introduction to Functional-Differential Equations. Applied Mathematical Sciences, vol. 99. Springer, New York (1993).
12. Hartung, F.: Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174(2), 201-122 (2005).
13. Hartung, F., Herdman, T. L., Turi, J.: Parameter identification in classes of neutral differential equations with state-dependent delays. Nonlinear Anal. 39(3), 305-325 (2000).
14. Hernández, E., Henríquez, H.: Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221(1), 499-522 (1998).
15. Hernández, E., Henríquez, H.: Existence results for partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221(2), 452-475 (1998).
16. Hernández, E., Mckiben, M.: On state-dependent delay partial neutral functional differential equations. Appl. Math. Comput. 180(1), 294-301 (2007).
17. Hernández, E., Pierri, M., Gonçalves, G.: Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comput. Math. Appl. 52, 411-420 (2006).
18. Hernández, E., Prokopczyk, A., Ladeira, L.: A note on partial functional differential equations with state-dependent delay. Nonlinear Anal., Real World Appl. 7(4), 510-519 (2006).
19. Hernández, E., Rabelo, M., Henríquez, H.: Existence of solutions for impulsive partial neutral functional differential equations. J. Math. Anal. Appl. 331, 1135-1158 (2007).
20. Hernández, E., McKibben, M., Henríquez, H. R.: Existence results for abstract impulsive second order neutral functional differential equations. Nonlinear Anal. (2008). doi: 10. 1016/j. na. 2008. 03. 062.
21. Hino, Y., Murakami, S., Naito, T.: Functional-Differential Equations with Infinite Delay. Lectures Notes in Mathematics, vol. 1473. Springer, New York (2003).
22. Lakshmikanthan, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. Modern Applied Mathematics, vol. 6. World Scientific, Teaneck (1989).
23. Luo, Z., Shen, J.: Stability results for impulsive functional differential equations with infinite delays. J. Comput. Appl. Math. 131(1/2), 55-64 (2001).
24. Martin, H. R.: Nonlinear Operators and Differential Equations in Banach Spaces. Krieger, Florida (1987).
25. Necas, J.: Les Méthodes Directes en Théorie des Équations Elliptiques. Masson, Paris (1967).
26. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44. Springer, New York (1983).
27. Rezounenko, A.: Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions. arXiv: 0801. 4715v2 (2008).
28. Samoilenko, A. M., Perestyuk, N. A.: Impulsive Differential Equations,. World Scientific, Singapore (1995).
29. p(0, T, B). Ann. Math. Pura Appl. CXLVI, 65-96 (1987).
30. Willé, D., Baker, C.: Stepsize control and continuity consistency for state-dependent delay-differential equations. J. Comput. Appl. Math. 53(2), 163-170 (1994).
31. Wu, J.: Theory and Applications of Partial Functional-Differential Equations. Applied Mathematics Sciences, vol. 119. Springer, New-York (1996).
32. Wu, J., Rozounenko, A.: A non-local PDE model for population dynamics with state selective delay: local theory and global attractors. J. Comput. Appl. Math. 190(1-3), 99-113 (2006).
33. Yang, Z., Cao, J.: Existence of periodic solutions in neutral state-dependent delays equations and models. J. Comput. Appl. Math. 174(1), 179-199 (2005).