Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 2, Issue 3, December 2018, Pages: 32-49

Results for impulsive perturbed evolution partial neutral functional differential equations in Frechet spaces

K. Karthikeyan1* and G.S. Murugapandian2

1Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode-637215, Tamil Nadu, India.
2Department of Mathematics, K.S.R. College of Engineering, Tiruchengode 637 215, Tamil Nadu, India.


In this paper, we prove the solvability of mild solutions for first-order impulsive evolution neutral functional perturbed differential equations with infinite delay. Our main tools are the nonlinear alternative proved by Avramescu for the sum of contractions and completely continuous maps in Frechet spaces and the semigroup theory.


Perturbed neutral impulsive differential equations, fixed point theory, nonlinear alternative, infinite delay, Frechet spaces.



1 N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, 246. Longman Scientific and Technical, Harlow John Wiley and Sons, Inc., New York, 1991

2 N.U. Ahmed, Dynamic systems and control with Applications, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.

3. Akca Haydar, Boucherif Abdelkadar, Valery Covachev, Impulsive functional differential equations with nonlocal conditions, Int. J. Math. Math. Sci. 29(2002) 251-256.

4. A. Anguraj and K. Karthikeyan, Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Analysis TMA 70(2009)2717-2721.

5. C. Avramescu, Some remarks on a fixed point theory of Krasnoselskii, Electronic J. Qual. The Diff. Equa., 5 (2003), 1-15.

6. S. Baghli, M. Benchohra, Perturbed functional and neutral functional evolution equations with infinite delay in Frechet spaces, Electronic J. Diff. Equa., 2008(2008), pp. 1-19.

7. M. Benchohra, J. Henderson, S.K. Ntouyas, Existence results for impulsive semilinear neutral functional differential equations in Banach spaces, Mem. Differential Equations Math. Phys. 25 (2002) 105-120.

8. Y.K. Chang, A.Anguraj and K.Karthikeyan, Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators, Nonlinear Analysis TMA 71(2009)4377-4386. 48K.Karthikeyan and G.S.Murugapandian

9. C. Corduneanu and Lakshmikantham, Equations with unbounded delay, Nonlinear Anal., 4 (1980), 831-877.

10. J.R. Graef and A. Ouahab, Some existence and uniqueness results for first order Boundary value problems for impulsive functional differential equations with infinite delay in Frechet spaces, International Journal of Mathematics and Mathematical Sciences, (2006), 1-16.

11. J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21(1978), 11-41.

12. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differtial Equations, Applied Mathematical Sciences 99, Springer-Verlag, New York, 1993.

13. E. Hernandez, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292(2004), 194-210.

14. Y. Hino, S. Murakami, and T. Naito, Functional differential equations with infinite delay, Lecture notes in Math., 1473, Springer-Verlag, Berlin, 1991.

15. F. Kappel and W. Schappacher, Some considerations to the fundamental theory of infinite delay equations, J. Differential Equations, 37(1980), 141-183.

16. V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of impulsive Differential Equations, World Scientific, Singapore, 1989.

17. S.K. Ntouyas, Existence results for impulsive partial neutral functional differential inclusions, Electron. J. Differential Equations 2005, 30 (2005), 1-11.

18. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

19. A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.

20. K. Schumacher, Existence and continuous dependence for differential equations with unbounded delay, Arch. Rational Mech. Anal., 64 (1978), 315-335.

21. J. Wu, Theory and Applications of Partial Functional Differential Equations, Applied Mathematical Sciences 119, Springer-Verlag, New York, 1996.

22. B. Yan, Boundary value problems on the half-line with impulses and infinite delay, J. Math. Anal. Appl. 259 (2001), 94-114.

Visitors count

Join us