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 (288.7 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

Results on homoclinic solutions of a partial difference equation involving the mean curvature operator

Yuhua Long1,2( ), Sha Li1,2
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Show Author Information

Abstract

By variational technique coupled with the mountain pass lemma and fountain theorem, we investigate a second-order partial difference equation involving the mean curvature operator in the present paper. We establish a number of criteria to guarantee the existence of multiple nontrivial homoclinic solutions. Our results generalize and improve some known ones. Additionally, two examples are provided to demonstrate applications of our obtained results.

Keywords

variational techniquemountain pass lemmafountain theorempartial difference equationhomoclinic solutionmean curvature operator
CLC number: Primary: 39A14; Secondary: 34C37

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 6429-6447
DOI: 10.3934/math.2025293

{{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:
Long Y, Li S. Results on homoclinic solutions of a partial difference equation involving the mean curvature operator. AIMS Mathematics, 2025, 10(3): 6429-6447. https://doi.org/10.3934/math.2025293

150

Views

0

Downloads

2

Crossref

2

Web of Science

2

Scopus
Received: 25 November 2024
Revised: 20 February 2025
Accepted: 18 March 2025
Published: 15 March 2025
©2025 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)