Mathematical Problems in Engineering
Volume 3 (1998), Issue 6, Pages 555-571

Variational Lyapunov method and stability theory

V. Lakshmikantham,1 X. Liu,1,3 and S. Leela2

1Florida Institute of Technology, Applied Mathematics Program, Melbourne 32901, FL, USA
2SUNY at Geneseo, Department of Mathematics, Geneseo 14454, NY, USA
3University of Waterloo, Department of Applied Mathematics, Waterloo N2L 3G1, Ontario, Canada

Received 15 July 1997

Copyright © 1998 V. Lakshmikantham 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.


By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.