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.
Original language | English |
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Pages (from-to) | 1-6 |
Number of pages | 6 |
Journal | Electronic Journal of Differential Equations |
Volume | 2009 |
Publication status | Published - 2 Jan 2009 |
Keywords
- Controllability
- Fixed point theorem
- Semilinear differential equations