文章基本信息

标题：QUALITATIVE PROPERTIES OF SOLUTIONS OF RICCATI'S α-DIFFERENCE EQUATIONS
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作者：Manuel, M. Maria Susai ; Chandrasekar, V. ; Xavier, G. Britto Antony 等
期刊名称：International Journal of Differential Equations and Applications
印刷版ISSN：1311-2872
出版年度：2012
卷号：11
期号：2
DOI：10.12732/ijdea.v11i2.535
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：In this paper, by introducing $\alpha$-difference equation with the definition of generalized $\alpha$-difference operator, we discuss the general properties and boundedness behaviour of solutins of the generalized Riccati's $\alpha$-difference equation\begin{equation}{\label{ricc.01}}p(k)u(k+\ell)+\alpha^2 p(k-\ell)u(k-\ell)=\alpha q(k)u(k), k\in[\ell, \infty),\end{equation}where the real valued functions $p$ and $q$ are defined on $[\ell,\infty)$ and $p(k)>0$ for all $k\in[\ell,\infty)$. Equation (\ref{ricc.01}) equivalently can be written as\begin{equation}{\label{ricc.02}}-\Delta_{\alpha(\ell)}\Big(p(k-\ell)\Delta_{\alpha(\ell)}u(k-\ell)\Big)+\alpha f(k)u(k)=0, k\in[\ell,\infty),\end{equation}where $f(k)=q(k)-p(k)-p(k-\ell)$.
关键词：generalized α-difference operator, generalized α-difference equation;39A10, 39A11, 39A20