Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 142, pp. 1-15.
Title: Exact controllability of generalized Hammerstein type integral
equation and applications
Authors: Dimplekumar N. Chalishajar (Gujarat Univ., Vasad, India)
Raju K. George (Univ. of Delaware, Newark, DE, USA}
Abstract:
In this article, we study the exact controllability of an abstract
model described by the controlled generalized Hammerstein type
integral equation
$$
x(t) = \int_0^t h(t,s)u(s)ds+ \int_0^t k(t,s,x)f(s,x(s))ds,
\quad 0 \leq t \leq T <\infty,
$$
where, the state $x(t)$ lies in a Hilbert space $H$ and
control $u(t)$ lies another Hilbert space $V$ for each time
$t \in I=[0,T]$, $T>0$. 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.