Controllability of semilinear functional integrodifferential systems in Banach spaces

Controllability of nonlinear systems represented by ordinary differential equations in infinite-dimensional spaces has been extensively studied by several authors. Naito [12,13] has studied the controllability of semilinear systems whereas Yamamoto and Park [19] discussed the same problem for parabolic equation with uniformly bounded nonlinear term. Chukwu and Lenhart [3] have studied the controllability of nonlinear systems in abstract spaces. Do [4] and Zhou [20] investigated the approximate controllability for a class of semilinear abstract equations. Kwun et al [7] established the approximate controllability for delay Volterra systems with bounded linear operators. Controllability for nonlinear Volterra integrodifferential systems has been studied by Naito [14]. Recently Balachandran et al [1,2] studied the controllability and local null controllability of Sobolev-type integrodifferential systems and functional differential systems in Banach spaces by using Schauder's fixed-point theorem. The purpose of this paper is to study the controllability of semilinear functional integrodifferential systems in Banach spaces by using the Schaefer fixed-point theorem. The semilinear functional integrodifferential equation considered here serves as an abstract formulation of partial functional integrodifferential equations which arise in heat flow in material with memory [5,6,8,9,18].