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Exact controllability of generalized Hammerstein type integral equation and applications
oleh: Dimplekumar N. Chalishajar, Raju K. George
Format: | Article |
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Diterbitkan: | Texas State University 2006-11-01 |
Deskripsi
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.