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Journal of Function Spaces and Applications
Volume 2 (2004), Issue 1, Pages 71-95

The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems

1Department of Mathematics, Royal Military College of Canada, P.O. Box 17000 STN Forces, Kingston, Ontario, K7K 7B4, Canada
2Department of Mathematics and Statistics, Queen's University, Jeffery Hall, Kingston, Ontario, K7L 3N6, Canada

Received 1 November 2002

Academic Editor: Lars-Erik Persson

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.