Asymptotic Behavior of Solutions of Generalized Nonlinear $α$-difference Equation of Second Order (Journal of Informatics and Mathematical Sciences, 2013)
In this paper, the authors discuss the asymptotic behavior of solutions of the generalized nonlinear $\alpha$-difference equation\begin{equation}\Delta_{\alpha(\ell)}(p(k)\Delta_{\alpha(\ell)} u(k))+f(k)F(u(k))=g(k),\end{equation}$k\in[a,\infty),$ where the functions $p$, $f$, $F$ and $g$ are defined in their domain of definition and $\alpha>1$, $\ell$ is positive real.\ Further, $uF(u)>0$ for $u eq0$, $p(k)>0$ for all $k\in[a,\infty)$ for some $a\in[0,\infty)$ and for all $0\leq j
Keywords: Generalized difference equation; Generalized difference operator; Oscillation and nonoscillation