Abstract
This book is concerned with the problem of determining the asymptotic behavior of solutions of non-autonomous systems of linear differential and linear difference equations. It has been observed from the work by Poincaré and Perron that there is a very close and symbiotic relationship between many results for differential and difference equations, and we wish to further demonstrate this by treating the asymptotic theories here in parallel. In Chaps. 2, 4, 6, and 8 we will discuss topics related to asymptotic behavior of solutions of differential equations, and in Chaps. 3, 5, 7, and 9 some corresponding results for difference equations. In Chap. 10 we will show how some of these results can be simultaneously treated within the framework of so-called dynamic equations on time scales.
Keywords
- Asymptotic Behavior
- Difference Equation
- Asymptotic Representation
- Dichotomy Condition
- Contraction Mapping Principle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Bodine, S., Lutz, D.A. (2015). Introduction, Notation, and Background. In: Asymptotic Integration of Differential and Difference Equations. Lecture Notes in Mathematics, vol 2129. Springer, Cham. https://doi.org/10.1007/978-3-319-18248-3_1
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DOI: https://doi.org/10.1007/978-3-319-18248-3_1
Publisher Name: Springer, Cham
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