Geodesic
Exact controllability of generalized Hammerstein type integral equation and applications
Electronic journal of differential equations, Tome 2006 (2006)
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 
@article{EJDE_2006__2006__a148,
     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},
     year = {2006},
     volume = {2006},
     zbl = {1128.93004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a148/}
}
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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__a148/