Article Contents

2022, Volume 11, Issue 1: 67-93. Doi: 10.3934/eect.2020103

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Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces

1.
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India
2.
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India

^*Corresponding author: Jaydev Dabas
^*Corresponding author: Jaydev Dabas

Received: June 2020

Revised: September 2020

Early access: November 2020

Published: February 2022

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Abstract

In this paper, we consider the second order semilinear impulsive differential equations with state-dependent delay. First, we consider a linear second order system and establish the approximate controllability result by using a feedback control. Then, we obtain sufficient conditions for the approximate controllability of the considered system in a separable, reflexive Banach space via properties of the resolvent operator and Schauder's fixed point theorem. Finally, we apply our results to investigate the approximate controllability of the impulsive wave equation with state-dependent delay.

Keywords:

Impulsive functional differential equations,
approximate controllability,
Schauder's fixed point theorem,
cosine family,
resolvent operator.

Mathematics Subject Classification: 34K06, 34A12, 37L05, 93B05.

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