International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 281-311

Global existence and boundedness for quasi-variational systems

Giancarlo Cantarelli

Dipartimento di Matematica, Università degli studi di Parma, Via M. D'Azeglio 85/A , Parma 43100, Italy

Received 12 February 1997

Copyright © 1999 Giancarlo Cantarelli. 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 consider quasi-variational ordinary differential systems, which may be considered as the motion law for holonomic mechanical systems. Even when the potential energy of the system is not bounded from below, by constructing appropriate Liapunov functions and using the comparison method, we obtain sufficient conditions for global existence of solutions in the future and for their partial boundedness.