二阶微分方程系统求解极值映射不动点问题  

The second-order differential equation system for solving the fixed point problem of extremal mapping

作　　者：王莉 陈星旭 孙菊贺 杨峥 WANG Li;CHEN Xing-xu;SUN Ju-he;YANG Zheng(College of Science,Shenyang Aerospace University,Shenyang 110136,China;Mathematics Teaching and Research Section,Liaoning Experimental School,Shenyang 110031,China)

机构地区：[1]沈阳航空航天大学理学院,沈阳110136 [2]辽宁省实验学校数学教研组,沈阳110031

出　　处：《沈阳航空航天大学学报》2022年第1期77-84,共8页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:11801381)。

摘　　要：运用具有控制过程的二阶微分方程系统求解极值映射的不动点问题。运用对称函数和反对称函数的偏导数性质以及投影算子性质,证明了具有控制过程的二阶微分方程系统轨迹的聚点是极值映射不动点问题的解。最后给出两个算例说明二阶微分方程系统求解极值映射不动点问题的有效性。In this paper,the fixed point problem of extremal mapping was solved by using the second-order differential equation system with controlled process.Using the properties of partial derivatives of symmetric functions and antisymmetric functions and the properties of projection operators,the accumulation point of the trajectory of the second-order differential equation system with controlled process was proved to be the solution to the fixed point problem of extremal mapping.In the end,two examples were given to illustrate the effectiveness of second order differential equation system for solving the fixed point problem of extremal mapping.

关 键 词：二阶微分方程 极值映射 不动点 对称函数 反对称函数 

分 类 号：O224[理学—运筹学与控制论]