Geodesic
Some remarks on controllability of evolution equations in Banach spaces
Electronic journal of differential equations, Tome 2009 (2009)
In almost all papers in the literature, the results on exact controllability hold only for finite dimensional Banach spaces, since compactness of the semigroup and the bounded invertibility of an operator implies finite dimensional. In this note we show that the existence theory on controllability in the literature, can trivially be adjusted to include the infinite dimensional space setting, if we replace the compactness of operators with the complete continuity of the nonlinearity.
Classification : 93B05
Keywords: semilinear differential equations, controllability, fixed point theorem 
@article{EJDE_2009__2009__a125,
     author = {Ntouyas,  Sotiris K. and O'Regan,  Donal},
     title = {Some remarks on controllability of evolution equations in {Banach} spaces},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1168.93005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a125/}
}
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Ntouyas,  Sotiris K.; O'Regan,  Donal. Some remarks on controllability of evolution equations in Banach spaces. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a125/