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

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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