Journal of Inequalities and Applications
Volume 7 (2002), Issue 1, Pages 61-77
doi:10.1155/S102558340200005X

Lyapunov inequalities for time scales

Martin Bohner,1 Stephen Clark,1 and Jerry Ridenhour2

1Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla 65409-0020, MO, USA
2Department of Mathematics and Statistics, Utah State University, Logan 84322-3900, UT, USA

Received 10 April 2000; Revised 26 June 2000

Copyright © 2002 Hindawi Publishing Corporation. 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

The theory of time scales has been introduced in order to unify discrete and continuous analysis. We present a Lyapunov inequality for Sturm-Liouville dynamic equations of second order on such time scales, which can be applied to obtain a disconjugacy criterion for these equations. We also extend the presented material to the case of a general linear Hamiltonian dynamic system on time scales. Some special cases of our results contain the classical Lyapunov inequalities for differential equations as well as only recently developed Lyapunov inequalities for difference equations.