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March  2007, 18(2&3): 375-403. doi: 10.3934/dcds.2007.18.375

Lyapunov's second method for nonautonomous differential equations

Lars Grüne 1, , Peter E. Kloeden 2, , Stefan Siegmund 2, and  Fabian R. Wirth 3,

1. 

Mathematisches Institute, Universität Bayreuth, 95440 Bayreuth
2. 

Institut für Computerorientierte Mathematik, J.W. Goethe Universität, 60054 Frankfurt, Germany, Germany
3. 

The Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland

Received  April 2006 Revised  August 2006 Published  March 2007

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: nonautonomous attractor., nonautonomous differential equation, Lyapunov's second method, nonautonomous dynamical system, Lyapunov function, stability.
Mathematics Subject Classification: 37B25, 37B55, 93D3.
Citation: Lars Grüne, Peter E. Kloeden, Stefan Siegmund, Fabian R. Wirth. Lyapunov's second method for nonautonomous differential equations. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 375-403. doi: 10.3934/dcds.2007.18.375
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