一类半线性微分方程温和解的精确可控性  

Exact Controllability of Mild Solutions for a Class of Semilinear Differential Equations

作　　者：李建利 陈丽珍[2] 李刚[3] LI Jianli;CHEN Lizhen;LI Gang(Department of Mathematics,Taiyuan University,Taiyuan,Shanci,030032,P.R.China;School of Applied Mathematics,Shanri University of Finance and Economics,Taiyuan,Shanri,030006,P.R.China;School of Mathematical Sciences,Yangzhou University,Yangzhou,Jiangsu,225002,P.R.China)

机构地区：[1]太原学院数学系,山西太原030032 [2]山西财经大学应用数学学院,山西太原030006 [3]扬州大学数学科学学院,江苏扬州225002

出　　处：《数学进展》2024年第1期142-150,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11871064,11571300);山西省自然科学基金(Nos.201901D211412,202203021211334);太原学院院级科研项目(No.23TYYB05)。

摘　　要：本文利用非紧测度研究了Banach空间中非局部项满足Lipschitz连续条件下半线性微分方程温和解的精确可控性.在研究过程中没有使用以往文献中关于非紧测度假设的正则性条件,而是利用不同拓扑空间中非紧测度的估计,并利用商空间的性质给出了合适的控制函数,得到了微分方程温和解的精确可控性.因此,我们的研究结果可以认为是可控性领域结论的推广.In this paper,by using the noncompact measures,we study the exact controllability of mild solutions for semilinear differential equation with nonlocal condition when the nonlocal term is Lipschitz continuous in general Banach space.Here,we do not use the regularity condition of noncompact measure assumption in previous literatures,but use the estimate of noncompact measure in different topological spaces,and give the proper control function by the property of quotient space,and the exact controllability of the differential equation is obtained.Therefore,our results can be regarded as a generalization of the controllability field.

关 键 词：精确可控性 非紧测度 半线性微分方程 非局部条件 

分 类 号：O177.2[理学—数学]