Electron. J. Diff. Eqns.,
Vol. 2009(2009), No. 79, pp. 16.
Some remarks on controllability of evolution equations in
Banach spaces
Sotiris K. Ntouyas, Donal O'Regan
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.
Show me the PDF file (170 KB),
TEX file, and other files for this article.

Sotiris K. Ntouyas
Department of Mathematics,
University of Ioannina
451 10 Ioannina, Greece
email: sntouyas@uoi.gr


Donal O'Regan
Department of Mathematics, National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie 
Return to the EJDE web page