On the Difference Equation xn+1=α+xn−m/xnk

Qualitative behavior of rational difference equations of higher order

“…See also ([10], [11], [12], [13], [14], [15], [16], [17], [18]). Other related results can be found in ( [19], [20], [21], [22], [23], [24], [25], [27], [28], [29], [30], [31], [32]). Let us introduce some basic definitions and some theorems that we need sequel.…”

On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$

“…In recent years, difference equation research has attracted great interest from researchers. In particular, applications of higher-order non-linear difference equations have influenced many researchers (see [12], [13], [14], [15], [16], [17], [18], [19]). It is very important to examine especially the oscillation, the asymptotic behavior and the stability character of the solutions of the general classes of the higher-order non-linear difference equations, which have a complex structure and contain different states.…”

Global Attractivity of a Rational Difference Equation

“…Recently, there has been a great attention in studying nonlinear difference equations, see, for instance, [1], [3], [5], [10], [11], and references cited therein, as well as in studying systems of difference equations (see, e.g. [6], [9]).…”