%0 Journal Article
%T Exact Controllability of an Impulsive Semilinear System with Deviated Argument in a Banach Space
%A Sanjukta Das
%A Dwijendra N. Pandey
%A N. Sukavanam
%J Journal of Difference Equations
%D 2014
%R 10.1155/2014/461086
%X A functional differential equation with deviated argument coupled with impulsive conditions is studied for the existence and uniqueness of the mild solution and exact controllability of the system. The results are obtained by using Banach contraction principle and semigroup theory without imposing additional assumptions such as analyticity and compactness conditions on the generated semigroup and the nonlinear term. An example is provided to illustrate the presented theory. 1. Introduction It is possible to steer various dynamical systems from an arbitrary initial state to final state using the set of admissible controls. Such systems are called controllable. The theory for abstract linear control systems in finite-dimensions is well established. Many authors have extended the theory to infinite dimensional systems represented by nonlinear evolution equations. References of which are available in various articles such as [1¨C4]. As the change of state occurs abruptly in several physical phenomena, many authors have discussed impulsive differential equations in their articles. For instance, Chang [5] and Li et al. [6] discussed the controllability of impulsive functional differential system in Banach spaces using Schaefer¡¯s fixed point theorem. Jeong et al. [7] investigated the controllability of semilinear retarded control systems in Hilbert spaces. Tai and Wang [8] proposed sufficient conditions for the controllability of fractional impulsive neutral functional integrodifferential systems in a Banach space. Sakthivel and Anandhi [9] discussed approximate controllability of impulsive differential equations with state dependent delay. Controllability results are available in overwhelming majority for abstract impulsive differential systems rather than for impulsive functional differential equation with deviated arguments. As demand for efficient dynamic performances increase, mathematical models are required to behave more like real processes. Models are designed to deal with aftereffect, hereditary systems, equations with deviated arguments, and so forth. Delay differential systems are still resistant to quite a number of ¡°classical controllers.¡± Many partial differential systems can be reduced to functional differential equations with deviated arguments. Thus controllability of functional differential equation with deviated argument has to be extensively studied. However, Gal [10] studied the existence and uniqueness of local and global solutions for initial value problem with deviated argument Pandey et al. [11] used analytic semigroup theory and fixed
%U http://www.hindawi.com/journals/jde/2014/461086/