Asymptotic Solutions of nonlinear difference equations
TLDR
In this article, the authors studied the asymptotics of first-order nonlinear difference equations and provided sufficient conditions for the existence of an actual solution with such as-ymptotic behaviour.Abstract:
¯We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.read more
Citations
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Journal ArticleDOI
Asymptotics of families of solutions of nonlinear difference equations
TL;DR: Several types of attraction and repulsion are identified, which range from almost orthogonality to almost parallelness, and necessary and sufficient conditions for these types of behaviour are given.
Book ChapterDOI
A Radically Elementary Theory of Itô Diffusions and Associated Partial Differential Equations
TL;DR: In this paper, the authors consider the problem of computing the setminus of a setminus with respect to a pair of nodes, and show that a,b : \mathbf{R} \times [0,1] \rightarrow \mathBF{R}\).
References
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Book
An introduction to difference equations
TL;DR: In this article, the authors combine both analytic and geometric (topological) approaches to studying difference equations and integrate both classical and modern treatments of the subject, offering material stability, z-transform, discrete control theory and symptotic theory.
Journal ArticleDOI
Internal set theory: A new approach to nonstandard analysis
TL;DR: Internal set theory (1ST) as discussed by the authors is an approach to nonstandard analysis which is based on a theory which is called internal set theory, and it can be seen as an extension of the standard set theory.
Journal ArticleDOI
Sur les Equations Lineaires aux Differentielles Ordinaires et aux Differences Finies
Journal ArticleDOI
Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
TL;DR: In this paper, the authors asymptotically represent solutions of linear difference equations by transforming them into so-called L-diagonal form, and two properties are then responsible for the equivalence of an L-Diagonal form to a diagonal one: a dichotomy condition on the diagonal part, and a growth condition on perturbation term.