Advances in Difference Equations 
Volume 2006 (2006), Article ID 69106, 10 pages
doi:10.1155/ADE/2006/69106

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

Abstract

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.