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__a25,
     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__a25/}
}
TY  - JOUR
AU  - Ntouyas,  Sotiris K.
AU  - O'Regan,  Donal
TI  - Some remarks on controllability of evolution equations in Banach spaces
JO  - Electronic journal of differential equations
PY  - 2009
VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a25/
LA  - en
ID  - EJDE_2009__2009__a25
ER  - 
%0 Journal Article
%A Ntouyas,  Sotiris K.
%A O'Regan,  Donal
%T Some remarks on controllability of evolution equations in Banach spaces
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a25/
%G en
%F EJDE_2009__2009__a25
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__a25/