Mathematical Problems in Engineering 
Volume 3 (1998), Issue 6, Pages 555-571
doi:10.1155/S1024123X97000689

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

Abstract

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.