Opuscula Mathematica
Opuscula Math. 34, no. 3 (2014), 503-522

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.
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About the authors ▼
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
About the article ▼
Received: 2012-09-03.
Revised: 2013-05-28.
Accepted: 2013-11-15.
Cite this article as ▼
M. Mallika Arjunan, N. Y. Nadaf, Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay, Opuscula Math. 34, no. 3 (2014), 503-522, http://dx.doi.org/10.7494/OpMath.2014.34.3.503.
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