Existence and controllability results for damped second order impulsive neutral functional differential systems with state-dependent delay in Banach spaces

N.Y. Nadafa and M. Mallika Arjunanb,*

Existence and controllability results for damped second order impulsive neutral functional differential systems with state-dependent delay in Banach spaces

Authors :

N.Y. Nadaf^a and M. Mallika Arjunan^b,*

Author Address :

^aDepartment of Mathematics, Anjuman Institute of Technology and Management, Bhatkal–581320, Karnataka, India.
^bDepartment of Mathematics, C. B. M. College, Kovaipudur, Coimbatore–641 042, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive neutral functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.

Keywords :

Damped second order differential equations, impulsive neutral di.erential equations, controllability, state-dependent delay, cosine function, mild solution, fixed point.

DOI :

Article Info :

Received : October 11, 2012; Accepted : January 07, 2013.