一类差分方程组高阶导数的收敛性  

The Convergence of the Higher Order Derivative of a Kind of System of Difference Equations

作　　者：曹敏[1] 

机构地区：[1]南通纺织职业技术学院信息系,江苏南通226007

出　　处：《南通职业大学学报》2010年第3期70-72,共3页Journal of Nantong Vocational University

摘　　要：为证明G.Ladas对一类非线性差分方程的解有一定周期性的猜测,对一类非线性差分方程组的扰动解在稳定点的高阶导数的收敛性进行了研究。文章将该非线性差分方程转化为非线性差分方程组,同时给出了非线性差分方程组稳定点的定义,并证明了该非线性差分方程组的扰动解在稳定点高阶导数的整体收敛性。The convergence of the higher order derivative of the perturbing solutions for nonlinear difference equations at the stable point is an important tool in the study of the periodic solutions of the nonlinear difference equation.G.Ladas conjectured that a nonlinear difference equation has periodic solutions.In this paper,we turn this difference equation to a system of nonlinear difference equations,then give the definition of the stable point,and prove the global convergence of the higher order derivative of the perturbing solutions for the nonlinear difference equations at the stable point.

关 键 词：差分方程 高阶导数 整体收敛性 

分 类 号：O175.27[理学—数学]