International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 281-311
doi:10.1155/S0161171299222818

Global existence and boundedness for quasi-variational systems

Abstract

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.