Abstract and Applied Analysis
Volume 2004 (2004), Issue 12, Pages 1057-1079

Periodic solutions for nonautonomous differential equations and inclusions in tubes

Grzegorz Gabor

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, Torun 87-100, Poland

Received 6 September 2002

Copyright © 2004 Grzegorz Gabor. 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 study the existence of periodic trajectories for nonautonomous differential equations and inclusions remaining in a prescribed compact subset of an extended phase space. These sets of constraints are nonconvex right-continuous tubes not satisfying the viability tangential condition on the whole boundary. We find sufficient conditions for existence of viable periodic trajectories studying properties of the exit subset of the tube. A new approximation approach for continuous multivalued maps is presented.