Opuscula Math. 34, no. 3 (2014), 503-522
http://dx.doi.org/10.7494/OpMath.2014.34.3.503
Opuscula Mathematica
Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
M. Mallika Arjunan
N. Y. Nadaf
Abstract. In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive 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 differential equations, controllability, state-dependent delay, cosine function, mild solution, fixed point.
Mathematics Subject Classification: 34A37, 93B05.
- M. Mallika Arjunan
- C.B.M. College, Department of Mathematics, Kovaipudur, Coimbatore-641 042, Tamil Nadu, India
- N. Y. Nadaf
- Government PU College, Department of Mathematics, Vidyanagar, Hungund-587118, Bagalkot, Karnataka, India
- Received: 2012-09-03.
- Revised: 2013-05-28.
- Accepted: 2013-11-15.
