Existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions

被引：4

作者：

Wang, Song ^{[1
]}

Shu, Xiao-Bao ^{[1
]}

Shu, Linxin ^{[1
]}

机构：

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

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 05期

关键词：

damped random impulsive differential equations; mild solution; mountain pass lemma; minimax principle; theoery of critical point; energy functional; EXPONENTIAL STABILITY; PERIODIC-SOLUTIONS; SYSTEMS; CONTROLLABILITY;

D O I：

10.3934/math.2022431

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study sufficient conditions for the existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions. By using variational method we first obtain the corresponding energy functional. Then the existence of critical points are obtained by using Mountain pass lemma and Minimax principle. Finally we assert the critical point of enery functional is the mild solution of damped random impulsive differential equations.

引用

页码：7685 / 7705

页数：21

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