一类非线性时滞差分方程的全局吸引性  

Globally Attractivity of a Nonlinear Delay Difference Equation

作　　者：明亚东[1] 

机构地区：[1]山西大同大学数学与计算机科学学院,山西大同037009

出　　处：《中北大学学报（自然科学版）》2013年第3期223-225,230,共4页Journal of North University of China(Natural Science Edition)

基　　金：山西省高等学校科技研究开发项目(20111117)

摘　　要：研究了一类具有周期系数的非线性时滞差分方程.利用迭代算法和数学归纳法,论证了方程的初值问题的解的存在唯一性及解的有界性;利用不动点原理和数学归纳法,讨论了方程的正周期解的存在性;利用导数和极限的方法获得了方程关于正周期解的全局吸引性的充分条件.结论推广和改进了非线性时滞差分方程中系数为常数时的结果.A nonlinear delay difference equation with periodic coefficients was considered. Existence ancl uniqueness of initial value problem of the equation and boundedness of that every solution were demonstrated by iterate algorithm and mathematical induction the existence of a positive periodic solution of the equation was discussed by fixed point theorem and mathematical induetion sufficient condition for the global attractivity about positive periodic solution were obtained by using limit process and derivative method. The studies extend and improve the well-known results of the delay difference equation when the coefficients is const.

关 键 词：时滞差分方程 有界性 周期解 全局吸引性 

分 类 号：O175.7[理学—数学]