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 Electronic Research Archive Article
PDF (570.2 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

A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains

Abdeljabbar Ghanmi1( ), Hadeel Z. Alzumi1, Noureddine Zeddini2
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
Department of Mathematics, College of Science, Taibah University, Madinah, KSA
Show Author Information

Abstract

In this paper, we prove the existence of solutions for an elliptic system. More precisely, we combine the potential theory with the sub-super solution method and use the properties of the well-known Kato class to justify our existence results. The novelty of our study is that we consider either the bounded or the exterior domain; Also, the nonlinearities may be singular near the boundary. Some examples are presented to validate our main results.

Keywords

Green's functionelliptic systemsSchauder fixed point theoremsub-supersolutions method

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 32 Issue 6,
June 2024
Pages 3742-3757
DOI: 10.3934/era.2024170

{{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:
Ghanmi A, Alzumi HZ, Zeddini N. A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains. Electronic Research Archive, 2024, 32(6): 3742-3757. https://doi.org/10.3934/era.2024170

1

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 26 March 2024
Revised: 15 May 2024
Accepted: 31 May 2024
Published: 15 June 2024
©2024 the Author(s), licensee AIMS Press.

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