Abstract and Applied Analysis
Volume 2003 (2003), Issue 9, Pages 547-571

Bounded solutions of Carathéodory differential inclusions: a bound sets approach

Jan Andres,1 Luisa Malaguti,2 and Valentina Taddei3

1Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc 779 00, Czech Republic
2Department of Engineering Sciences and Methods, University of Modena and Reggio Emilia, Via Fogliani 1, Reggio Emilia 42100, Italy
3Department of Mathematics and Informatics, University of Udine, Viadelle Scienze 206, Udine 33100, Italy

Received 9 March 2002

Copyright © 2003 Jan Andres et al. 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.


A bound sets technique is developed for Floquet problems of Carathéodory differential inclusions. It relies on the construction of either continuous or locally ipschitzian Lyapunov-like bounding functions. Proceeding sequentially, the existence of bounded trajectories is then obtained. Nontrivial examples are supplied to illustrate our approach.