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

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.