Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 79, pp. 1-6.

Title: Some remarks on controllability of  evolution  equations in
       Banach spaces

Authors: Sotiris K. Ntouyas (Univ. of Ioannina, Greece)
         Donal O'Regan (National Univ. Galway, Ireland)

Abstract:
 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. 
 
Submitted May 1, 2009. Published June 24, 2009.
Math Subject Classifications: 93B05.
Key Words: Semilinear differential equations; controllability;
           fixed point theorem.