Department of Mathematics, University of Ioannina
451 10 Ioannina, Greece
email: sntouyas@uoi.gr
Department of Mathematics, National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie
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.
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Sotiris K. Ntouyas Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece email: sntouyas@uoi.gr |
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Donal O'Regan Department of Mathematics, National University of Ireland Galway, Ireland email: donal.oregan@nuigalway.ie |
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