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Math. Comput. Appl. 2018, 23(3), 32; https://doi.org/10.3390/mca23030032

Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses

1
Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA
2
School of Basic Sciences, Indian Institute of Technology Mandi, Kamand 175005, India
*
Author to whom correspondence should be addressed.
Received: 30 April 2018 / Revised: 15 June 2018 / Accepted: 16 June 2018 / Published: 21 June 2018
(This article belongs to the Section Natural Sciences)
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Abstract

In this manuscript, a stronger concept of exact controllability called Total Controllability has been introduced. Sufficient conditions have been established for the total controllability of the proposed problem. The proposed control problem is a second-order semi-linear differential equation with infinite delay and non-instantaneous impulses. The tools for study include the strongly continuous cosine family and Sadovskii’s fixed point theorem. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. In addition, the total controllability of an integrodifferential problem has been investigated. Finally, an example is provided to illustrate the analytical findings. View Full-Text
Keywords: infinite delay; non-instantaneous impulses; Sadovskii’s fixed point theorem; total controllability infinite delay; non-instantaneous impulses; Sadovskii’s fixed point theorem; total controllability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chalishajar, D.N.; Kumar, A. Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses. Math. Comput. Appl. 2018, 23, 32.

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