Advances in Difference Equations
Volume 2006 (2006), Article ID 69106, 10 pages

Lyapunov functions for linear nonautonomous dynamical equations on time scales

Peter E. Kloeden1 and Alexandra Zmorzynska2

1Institut für Mathematik, Johann Wolfgang Goethe Universit*#228;t, Frankfurt am Main 60054, Germany
2Institut für Mathematik, Technische Universität Berlin, Berlin 10623, Germany

Received 25 January 2006; Revised 23 March 2006; Accepted 13 April 2006

Copyright © 2006 Peter E. Kloeden and Alexandra Zmorzynska. 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.


The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time scale with uniformly bounded graininess.