一类推广的具有时滞的Pachpatte离散不等式及其应用  

A GENERALIZED PACHPATTE'S DISCRETE INEQUALITY WITH DELAYS AND ITS APPLICATIONS

作　　者：侯宗毅[1] 王五生[1] 

机构地区：[1]河池学院数学系,宜州546300

出　　处：《系统科学与数学》2009年第7期865-876,共12页Journal of Systems Science and Mathematical Sciences

基　　金：广西教育厅科学研究项目(200707MS112);广西教改项目(200710961);河池学院应用数学重点学科(200725);自然科学研究项目(2006N001);重点课程<数学建模(20089);教改项目(2006E006;2007E006);广西自然科学基金(200991265)项目资助

摘　　要：不仅把Pachpatte的离散不等式推广成时滞不等式,而且把不等式中的常数项推广成连续的正函数。推广后的不等式不仅包含了更多项,且不要求函数的单调性。利用单调化技巧给出了不等式中未知函数的估计。最后用得到的结果研究时滞差分方程初值问题解的唯一性与有界性。In this paper, Pachpatte＇s discrete inequality is generalized to a retarded form, where not only delays are included but the contant term is generalized to a positive function. In the generalized inequality, there are more complex terms and the monotonicity of given functions is not required. Estimation of unknown function in the inequality is given by a technique of monotonization. Finally, the result is applied to discuss boundedness and uniqueness of solution for the initial value problem of a delay difference equation.

关 键 词：离散不等式 单调性 时滞差分方程 有界性 唯一性 

分 类 号：O178[理学—数学] O175.7[理学—基础数学]