Hilbert格上分数阶微分变分不等式极大解与极小解的存在性  

Existence of Maximal and Minimal Solutions to Fractional Differential Variational Inequalities on Hilbert Lattices

作　　者：王月虎[1] 张从军[2] Yue Hu WANG;Cong Jun ZHANG(School of Management Science and Engineering,Nanjing University of Finance and Economics,Nanjing 210023,P.R.China;School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,P.R.China)

机构地区：[1]南京财经大学管理科学与工程学院,南京210023 [2]南京财经大学应用数学学院,南京210023

出　　处：《数学学报（中文版）》2021年第6期933-946,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(72001101,11401296);江苏省自然科学基金(BK20171041);江苏高校哲学社会学研究项目(2017SJB0238);江苏省高校自然科学研究面上项目(16KJB110009);江苏省青蓝工程;南京财经大学青年学者支持计划。

摘　　要：本文提出一种研究分数阶微分变分不等式的半序方法.在Hilbert格上利用序不动点定理证明了分数阶微分变分不等式极大解与极小解的存在性,获得一些新结果.这些半序方法与最近有关文献中的拓扑不动点定理和离散序列逼近法具有本质不同,能够有效削弱相关函数的连续性.We introduce a class of order-theoretic approaches for studying the fractional differential variational inequalities.By using the order-theoretic fixed point theorems,we prove the existence of maximal solution and minimal solution to fractional differential variational inequalities on Hilbert lattices,and obtain some new results.Our order-theoretic approaches adopted for this kind of problems are fundamentally different from the recent literatures,in which the main tools are the topological fixed point theorems and discrete approximation methods.These order-theoretic methods can effectively weaken the continuity of the involved mappings.

关 键 词：微分变分不等式 序不动点 极大解 极小解 

分 类 号：O177.91[理学—数学]