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Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 325-351

Topological structure of solution sets of differential inclusions: the constrained case

1Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, Torun 87-100, Poland
2Faculty of Mathematics, University of Lodz, ul. Banacha 22, Łódź 90-238, Poland

Received 11 March 2002

Copyright © 2003 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.


We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. Some new results concerning semilinear differential inclusions with state variables constrained to the so-called regular and strictly regular sets, together with their applications, are presented and discussed.