The asymptotic behavior of a class of nonlinear delay difference equations

Sedaghat, Hassan; Wang, Wendi

doi:10.1090/S0002-9939-00-05974-8

The asymptotic behavior of a class of nonlinear delay difference equations
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by Hassan Sedaghat and Wendi Wang PDF

Proc. Amer. Math. Soc. 129 (2001), 1775-1783 Request permission

Abstract:

The asymptotic behavior of difference equations of type \begin{equation*} x_{n}=x_{n-1}^{p}[1+g(\sum _{i=1}^{m}f_{i}(x_{n-i}))],\quad p>0, \end{equation*} is studied, where $g$ and each $f_{i}$ are continuous real functions with $g$ decreasing and $f_{i}$ increasing. Results include sufficient conditions for permanence, oscillations and global attractivity.

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