Controllability of Urysohn integral inclusions of Volterra type

Abstract

The aim of this paper is to study the controllability of a system described by an integral inclusion of Urysohn type with delay. In our approach we reduce the controllability problem of the nonlinear system into solvability problem of another integral inclusion. The solvability of this integral inclusion is subsequently established by imposing suitable standard boundedness, convexity and semicontinuity conditions on the set-valued mapping defining the integral inclusion, and by employing Bohnenblust-Karlin extension of Kakutani's fixed point theorem for set-valued mappings.

Keywords

• Controllability
• Urysohn operator
• delay systems
• set-valued mappings
• Kakutani's Fixed-point theorem