In the paper, we study weak invariance of differential inclusions with non-fixed time impulses under compactness type assumptions. When the right-hand side is one sided Lipschitz an extension of the well known relaxation theorem is proved. In this case also necessary and sufficient condition for strong invariance of upper semi continuous systems are obtained. Some properties of the solution set of impulsive system (without constrains) in appropriate topology are investigated.
Submitted March 27, 2006. Published May 26, 2006.
Math Subject Classifications: 34A60, 34A37, 34B15, 49K24.
Key Words: Impulsive differential inclusions; constrains; invariant solutions.
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| Tzanko Donchev |
Department of Mathematics
University of Architecture and Civil Engineering
1 "Hr. Smirnenski" str., 1046 Sofia, Bulgaria
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