Electron. J. Diff. Eqns., Vol. 2009(2009), No. 79, pp. 1-6.

Some remarks on controllability of evolution equations in Banach spaces

Sotiris K. Ntouyas, Donal O'Regan

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.

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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

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