具有最大项的集值微分方程初边值问题的平均法  

Averaging Method for Initial and Boundary Value Problems of Set-valued Differential Equations with Maxima

作　　者：王培光[1] 李贝贝 Pei Guang WANG;Bei Bei LI(College of Mathematics and Information Science,Hebei University,Baoding 071002,P.R.China)

机构地区：[1]河北大学数学与信息科学学院,保定071002

出　　处：《数学学报（中文版）》2023年第6期1057-1070,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12171135,11771115)。

摘　　要：本文研究了具有最大项的集值微分方程初边值问题解的渐近性.我们通过引入Hausdorff度量和半离差度量的概念,应用平均法分别讨论了当方程右端函数平均极限存在和不存在两种情况下,原方程与平均方程解之间的渐近关系.We investigate the asymptotic approximation of solutions of initial and boundary value problems for set-valued differential equations with maxima.By introducing the concepts of Hausdorff measure and semideviation measure,the approximate relationship of the solutions between the original equations and the average equations is discussed via the averaging method when the average limit of the right-hand function exists or does not exist.

关 键 词：集值微分方程 最大项 初边值问题 平均法 

分 类 号：O175.13[理学—数学] O177.92[理学—基础数学]