Oscillatory and Asymptotic Behavior of Higher Order Nonlinear Difference Equations

We shall present new oscillation and asymptotic behavior criteria of higher order nonlinear difference equations of the form Δ(a(t)Δn-1x(t)α+q(t)xβ(t-m+1)=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Delta \left( ({a(t)}\left( {\Delta ^{n-1}{x(t)}} \right) ^{\alpha } \right) +{q(t)x}^{\beta }({t}-{m}+1)=0, \end{aligned}$$\end{document}with nonnegative real coefficients.