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
2t, Frankfurt am Main 60054, Germany
3Institut für Mathematik, Technische Universität Berlin, Berlin 10623, Germany
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.