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Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 49431, 7 pages
doi:10.1155/JAMSA/2006/49431

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

Abstract

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.