AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (275.5 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

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

Song Wang, Xiao-Bao Shu( ), Linxin Shu
School of Mathematics, Hunan University, Changsha, Hunan 410082, China
Show Author Information

Abstract

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.

Keywords

damped random impulsive differential equationsmild solutionmountain pass lemmaminimax principletheoery of critical pointenergy functional
CLC number: 34B37, 37H10, 37J51

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7685-7705
DOI: 10.3934/math.2022431

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Wang S, Shu X-B, Shu L. Existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions. AIMS Mathematics, 2022, 7(5): 7685-7705. https://doi.org/10.3934/math.2022431

41

Views

0

Downloads

3

Crossref

4

Web of Science

4

Scopus
Received: 09 August 2021
Revised: 17 January 2022
Accepted: 24 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)