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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Lyapunov's second method for nonautonomous differential equations

Pages: 375 - 403, Volume 18, Issue 2/3, June/July 2007      doi:10.3934/dcds.2007.18.375

 
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Lars Grüne - Mathematisches Institute, Universität Bayreuth, 95440 Bayreuth, Germany (email)
Peter E. Kloeden - Institut für Computerorientierte Mathematik, J.W. Goethe Universität, 60054 Frankfurt, Germany (email)
Stefan Siegmund - Institut für Computerorientierte Mathematik, J.W. Goethe Universität, 60054 Frankfurt, Germany (email)
Fabian R. Wirth - The Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland (email)

Abstract: Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems.

Keywords:  Lyapunov function, Lyapunov's second method, nonautonomous dynamical system, nonautonomous differential equation, stability, nonautonomous attractor.
Mathematics Subject Classification:  37B25, 37B55, 93D30.

Received: April 2006;      Revised: August 2006;      Available Online: March 2007.