Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 49431, 7 pages

Generalized flow invariance for differential inclusions

T. Gnana Bhaskar and V. Lakshmikantham

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 6 May 2004; Revised 12 May 2005; Accepted 12 May 2005

Copyright © 2006 T. Gnana Bhaskar and V. Lakshmikantham. 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.


We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized sense are presented.