Opuscula Math. 34, no. 3 (2014), 503-522
Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
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.
- Received: 2012-09-03.
- Revised: 2013-05-28.
- Accepted: 2013-11-15.