The existence of upper and lower solutions to second order random impulsive differential equation with boundary value problem

被引：22

作者：

Li, Zihan ^{[1
]}

Shu, Xiao-Bao ^{[1
]}

Xu, Fei ^{[2
]}

机构：

[1] Hunan Univ, Coll Math, Changsha 410082, Hunan, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 06期

关键词：

random impulse differential equation; upper and lower solutions; monotonic iterative sequences; boundary value problem; EXPONENTIAL ULTIMATE BOUNDEDNESS; MULTIPLE POSITIVE SOLUTIONS; STABILITY; CONTROLLABILITY; SYSTEMS; DELAY;

D O I：

10.3934/math.2020398

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the existence of upper and lower solutions to a second-order random impulsive differential equation. We first study the solution form of the corresponding linear impulsive system of the second-order random impulsive differential equation. Based on the form of the solution, we define the resolvent operator. Then, we prove that the fixed point of this operator is the solution to the equation. Finally, we construct the sum of two monotonic iterative sequences and prove that they are convergent. Thus, we conclude that the system has upper and lower solutions.

引用

页码：6189 / 6210

页数：22

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