Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay

Abstract

This paper is concerned with controllability of a partial neutral functional differential inclusion of second order with impulse effect and infinite delay. We introduce a new phase space to prove the controllability of an inclusion which consists of an impulse effect with infinite delay. We claim that the phase space considered by different authors is not correct. We establish the controllability of mild solutions using a fixed point theorem for contraction multi-valued maps and without assuming compactness of the family of cosine operators.Keywords Controllability · Second order impulsive neutral differential inclusions · Fixed point theorem for multi-valued maps · Strongly continuous cosine family

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

“…Often, it has been assumed that the delays are either fixed constants or distributed delays. In recent years, many papers have been published on time delay of both kinds, finite as well as infinite [9][10][11][12][13] .…”

A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

“…[22][23][24]. The study of dynamical systems with impulsive effects has been an object of investigations [25][26][27][28]. It has been extensively studied under various conditions on the operator A and the nonlinearity f by several authors [29][30][31].…”

“…It has been extensively studied under various conditions on the operator A and the nonlinearity f by several authors [29][30][31]. Chalishajar and Acharya studied controllability of neutral impulsive differential inclusion with nonlocal conditions [32], (see also [33][34][35][36]), Anguraj and Karthikeyan [37] discussed the existence of solutions for impulsive neutral functional differential equations with nonlocal conditions. Ahmad, Malar, and Karthikeyan [38] studied nonlocal problems of impulsive integro-differential equations with a measure of noncompactness.…”

Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay

“…Chalishajar [3] studied the exact controllability of impulsive partial neutral functional differential equations with infinite delay and S. Selvi and M. Mallika Arjunan [4] studied the exact controllability for impulsive differential systems with finite delay. For approximate controllability of impulsive semilinear evolution equation, Lizhen Chen and Gang Li [5] studied the approximate controllability of impulsive differential equations with nonlocal conditions, using measure of noncompactness and Monch Fixed Point Theorem, and assuming that the nonlinear term ( ) , f t z does not depend on the control variable.…”