Controllability of nonlocal impulsive functional integrodifferential evolution systems

Abstract

Abstract. In this paper, we establish a set of sufficient conditions for the controllability of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The controllability results are obtained with out assuming the compactness condition on the evolution operator by using the semigroup theory and applying the fixed point approach. An example is provided to illustrate the theory.

Schauder’s fixed-point theorem in approximate controllability problems

“…Impulsive neutral functional evolution integrodifferential system. A special case of the semilinear system is an impulsive neutral functional evolution integro-differential system given by (Radhakrishnan and Balachandran, 2011) …”

“…Definition 5. (Radhakrishnan and Balachandran, 2011) A function x(·) ∈ PC ((−∞, b], X) is called a mild solution of the dynamic system (3) if…”

“…(Radhakrishnan and Balachandran, 2011) The reachable set for the system (3) is described by the following formula:…”

“…Brought to you by | MIT Libraries Authenticated Download Date | 5/10/18 9:42 PM In order to examine approximate controllability of (3), the following assumptions should be introduced (Radhakrishnan and Balachandran, 2011).…”

“…The proof of the above theorem is based on Schauder's fixed-point theorem and presented by Radhakrishnan and Balachandran (2011).…”