Geodesic
Exact controllability of generalized Hammerstein type integral equation and applications
Electronic Journal of Differential Equations, Tome 2006 (2006).

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Summary: 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 $t \in I=[0,T], T$. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.
Classification : 93B05, 93C10
Keywords: exact controllability, Hammerstein type integral equation, monotone operator, solution operator 
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     author = {Chalishajar, Dimplekumar N. and George, Raju K.},
     title = {Exact controllability of generalized {Hammerstein} type integral equation and applications},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a48/}
}
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Chalishajar, Dimplekumar N.; George, Raju K. Exact controllability of generalized Hammerstein type integral equation and applications. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a48/