Electron. J. Diff. Equ., Vol. 2010(2010), No. 79, pp. 1-12.

Controllability of Urysohn integral inclusions of Volterra type

Thomas S. Angell, Raju K. George, Jaita Pankaj Sharma

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.

Submitted March 5, 2010. Published June 15, 2010.
Math Subject Classifications: 93B05, 93C10.
Key Words: Controllability; Urysohn operator; delay systems; set-valued mappings; Kakutani's Fixed-point theorem.

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Thomas S. Angell
Department of Mathematics, University of Delaware
Newark, DE 19716, USA
email: angell@math.udel.edu
Raju K. George
Department of Applied Mathematics
Faculty of Tech. & Engg., M.S. University of Baroda
Vadodara 390001, India
email: raju_k_george@yahoo.com
Jaita Pankaj Sharma
Department of Applied Mathematics
Faculty of Tech. & Engg., M.S. University of Baroda
Vadodara 390001, India
email: jaita_sharma@yahoo.co.uk

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