Abstract
The boundedness character of positive solutions of the following system of difference equations: $x_{n+1}=A+\frac{y^{p}_{n}}{x_{n-3}^{r}}$ , $y_{n+1}=A+\frac {x^{p}_{n}}{y_{n-3}^{r}}$ , $n\in{\mathbb{N}}_{0}$ , when $\min\{A,r\}>0$ and $p\ge0$ , is studied.
Highlights
Concrete nonlinear difference equations and systems, especially those which are not closely related to differential ones, have attracted a lot of attention recently
For the case p = q the system obviously becomes symmetric, that is, it is of the following form: xn = f, yn = f, n ∈ N, for some k, l ∈ N
A systematic study of positive solutions of nonlinear difference equations containing non-integer powers of their dependent variables began by Stević et al, approximately since the publication of [ ], where the first nontrivial results related to the Stevicet al
Summary
Concrete nonlinear difference equations and systems, especially those which are not closely related to differential ones, have attracted a lot of attention recently (see, for example, [ – ] and the references therein). The boundedness character of positive solutions of the following system of difference equations: xn+1 In [ ] Papaschinopoulos and Schinas studied the oscillatory behavior, the boundedness character, and the global stability of positive solutions of the following close to symmetric system of difference equations: xn+
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