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In the paper sufficient conditions for the difference equation :Δxn = Σi=0r an(i) xn+ito have a solution which tends to a constant, are given. Applying these conditions, an asymptotic formula for a solution of an m-th order equation is presented.

On the asymptotic behaviour of solutions of difference equations

J. Popenda (1988)

Annales Polonici Mathematici

On the asymptotic behaviour of the solutions of an n-th order difference equation

J. Popenda (1984)

Annales Polonici Mathematici

On the asymptotic integration of nonlinear dynamic equations.

Akın-Bohner, Elvan, Bohner, Martin, Djebali, Smaïl, Moussaoui, Toufik (2008)

Advances in Difference Equations [electronic only]

On the asymptotically periodic solution of some linear difference equations

Jerzy Popenda, Ewa Schmeidel (1999)

Archivum Mathematicum

For the linear difference equation $x_{n + 1} - a_{n} x_{n} = \sum_{i = 0}^{r} a_{n}^{(i)} x_{n + i}, n \in N$ sufficient conditions for the existence of an asymptotically periodic solutions are given.

On the asymptotics of mean value points for some finite-difference operators.

Nikonorov, Yu.G. (2002)

Sibirskij Matematicheskij Zhurnal

On the behavior of solutions of the system of rational difference equations: $x_{n + 1} = x_{n - 1} / (y_{n} x_{n - 1} - 1)$ , $y_{n + 1} = y_{n - 1} / (x_{n} y_{n - 1} - 1)$ , and $z_{n + 1} = z_{n - 1} / (y_{n} z_{n - 1} - 1)$ .

Kurbanli, Abdullah Selçuk (2011)

Discrete Dynamics in Nature and Society

On the behavior of the solutions to autonomous linear difference equations with continuous variable

Christos G. Philos, Ioannis K. Purnaras (2007)

Archivum Mathematicum

Autonomous linear neutral delay and, especially, (non-neutral) delay difference equations with continuous variable are considered, and some new results on the behavior of the solutions are established. The results are obtained by the use of appropriate positive roots of the corresponding characteristic equation.

On the behaviour of the solutions of a second-order difference equation.

Gutnik, Leonid, Stević, Stevo (2007)

Discrete Dynamics in Nature and Society

On the critical values of parametric resonance in Meissner's equation by the method of difference equations.

Hatvani, László (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On the difference equation $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}$

Elmetwally M. Elabbasy, Hamdy El-Metwally, E. M. Elsayed (2008)

Mathematica Bohemica

In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}, n = 0, 1, \dots$ where the parameters $a_{i}$ and $b_{i}$ for $i = 0, 1, \dots, k$ are positive real numbers and the initial conditions $x_{- k}, x_{- k + 1}, \dots, x_{0}$ are arbitrary positive numbers.

On the difference equation $x_{n + 1} = a x_{n} - b x_{n} / (c x_{n} - d x_{n - 1})$ .

Elabbasy, E.M., El-Metwally, H., Elsayed, E.M. (2006)

Advances in Difference Equations [electronic only]

On the difference equation $x_{n + 1} = \sum_{j = 0}^{k} a_{j} f_{j} (x_{n - j})$ .

Stević, Stevo (2007)

Discrete Dynamics in Nature and Society

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