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 |
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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 |
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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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