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

Arjunan M. M., Nadaf N. Y.

Opuscula Mathematica

2014

Vol. 34, no. 3

503--522

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.