Abstract
The concept of pullback convergence turned out to be a central idea to describe the long-term behavior of nonautonomous dynamical systems. This paper provides a general framework for the existence and structure of pullback attractors capturing the asymptotics of nonautonomous and order-preserving difference equations in Banach spaces. Furthermore we obtain criteria for the convergence to bounded entire solutions and additionally discuss various applications.
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Pötzsche, C. Order-preserving nonautonomous discrete dynamics: attractors and entire solutions. Positivity 19, 547–576 (2015). https://doi.org/10.1007/s11117-014-0315-3
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DOI: https://doi.org/10.1007/s11117-014-0315-3
Keywords
- Nonautonomous dynamical system
- Order-preserving dynamical system
- Pullback convergence
- Difference equation