Electron. J. Diff. Eqns., Vol. 2006(2006), No. 142, pp. 1-15.

Exact controllability of generalized Hammerstein type integral equation and applications

Dimplekumar N. Chalishajar, Raju K. George

Abstract:
In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation
$$ x(t) = \int_0^t h(t,s)u(s)ds+ \int_0^t k(t,s,x)f(s,x(s))ds, \quad 0 \leq t \leq T less than \infty, $$
where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t \in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Submitted April 23, 2006. Published November 9, 2006.
Math Subject Classifications: 93B05, 93C10.
Key Words: Exact controllability; Hammerstein type integral equation; monotone operator; solution operator.

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Dimplekumar N. Chalishajar
Department of Applied Mathematics
Sardar Vallabhbhai Patel Institute of Technology (SVIT)
Gujarat University, Vasad-388306. Gujarat State, India
email: dipu17370@yahoo.com, dimple.chalishajar@gmail.com
Raju K. George
Department of Mathematical Sciences
University of Delaware, Newark, DE 19716, USA
email: rkgeorgemsu@yahoo.com

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