逐段常变量微分方程的渐近概周期解  

Asymptotically almost periodic solution for differential equations with piecewise constant

作　　者：牛晶[1,2] 王似龙 

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025 [2]哈尔滨工业大学数学系,哈尔滨150001 [3]哈尔滨市呼兰区呼兰第六中学,哈尔滨150500

出　　处：《黑龙江大学自然科学学报》2010年第3期319-322,共4页Journal of Natural Science of Heilongjiang University

基　　金：中央高校基本科研业务费专项资金资助项目(HITNSRIF2009050)

摘　　要：给出概周期函数、渐近概周期函数及渐近概周期序列的定义,根据渐近概周期函数的性质,证明了逐段常变量差分方程的渐近概周期序列解的存在性和唯一性,最后利用此渐近概周期序列解,讨论了一类具有逐段常变量微分方程的渐近概周期解的存在性和唯一性。Firstly the definitions of almost periodic function, asymptotically almost periodic function and asymptotically almost periodic sequence are given. Then, it is shown that there exists a unique asymptotically almost periodic sequence solution of the difference equation by the property of asymptotically almost periodic function. Finally, the existence of differential equations with piecewise constant is discussed by applying the asymptotically almost periodic sequence solution.

关 键 词：渐近概周期序列 渐近概周期解 逐段常变量微分方程 

分 类 号：O177.2[理学—数学]