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

N.Y. Nadaf; M. Mallika Arjunan

doi:10.26637/mjm101/008

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 differential equations, controllability, state-dependent delay, cosine function, mild solution, fixed point.

Mathematics Subject Classification:

34A37, 93B05

Authors Imprint References Funding Related Articles Downloads

N.Y. Nadaf Department of Mathematics, Anjuman Institute of Technology and Management, Bhatkal–581320, Karnataka, India.
M. Mallika Arjunan Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore–641 042, Tamil Nadu, India. https://orcid.org/0000-0002-3358-0780

Pages: 70-85
Date Published: 01-01-2013
Vol. 1 No. 01 (2013): Malaya Journal of Matematik (MJM)

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