IJPAM: Volume 21, No. 2 (2005)

STABILITY IN A CLASS OF MONOTONE
NONLINEAR DIFFERENCE EQUATIONS

Hassan Sedaghat
Department of Mathematics
Virginia Commonwealth University
Richmond, VA 23284-2014, USA
e-mail: hsedagha@vcu.edu


Abstract.Conditions are given for the asymptotic stability of the unique equilibrium for difference equations of type

\begin{displaymath} x_{n}=f\left( \sum_{i=1}^{m}[a_{n-i}g\left( x_{n-i}\right) +g_{i}\left( x_{n-i}\right) ]\right) ,\quad n=1,2,3,\ldots\,, \end{displaymath}

in which the maps $f,g,g_{i}$ are all monotonic and the coefficients $a_{n-i}$ are non-negative and $m$-periodic.

Received: March 2, 2005

AMS Subject Classification: 39A11

Key Words and Phrases: asymptotic stability, monotonic maps, periodic coefficients, rational difference equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 2