Some remarks on controllability of evolution equations in banach spaces

Sotiris K. Ntouyas, Donal O'Regan

Research output: Contribution to a Journal (Peer & Non Peer)Articlepeer-review

24 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-6
Number of pages6
JournalElectronic Journal of Differential Equations
Volume2009
Publication statusPublished - 2 Jan 2009

Keywords

  • Controllability
  • Fixed point theorem
  • Semilinear differential equations

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