Abstract and Applied Analysis
Volume 2003 (2003), Issue 10, Pages 591-600
doi:10.1155/S1085337503209027
On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds
The Faculty of Mathematics, Voronezh State University, 1 University Square, Voronezh 394006, Russia
Received 27 August 2002
Copyright © 2003 Yuri E. Gliklikh and Andrei V. Obukhovskiĭ. 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.
Abstract
We consider second-order differential inclusions on a Riemannian manifold with lower semicontinuous right-hand sides. Several existence theorems for solutions of two-point boundary value problem are proved to be interpreted as controllability of special mechanical systems with control on nonlinear configuration spaces. As an application, a statement of controllability under extreme values of controlling force is obtained.