The periodicity and solutions of the rational difference equation with periodic coefficients
β Scribed by N. Taskara; K. Uslu; D.T. Tollu
- Book ID
- 108078773
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 227 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0898-1221
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π SIMILAR VOLUMES
Motivated by [1], we study the existence of periodic solutions of a perturbed continuous difference equation of first order without the assumptions of one-periodicity. Moreover, we generalize our results to the case of higher-order difference equations. We also give an algorithm to estimate the boun
tion theorems of the Leray Schauder type (see [6,9]). The aim of the present paper is to show that the same methodology can be adapted to prove the existence of periodic solutions for more general classes of equations and systems.
We consider the planar equation \(\dot{z}=\sum a_{k, l}(t) z^{k} \bar{z}^{l}\), where \(a_{k, l}\) is a \(T\)-periodic complex-valued continuous function, equal to 0 for almost all \(k, l \in \mathbb{N}\). We present sufficient conditions imposed on \(a_{k,}\), which guarantee the existence of its \