具有多点和多期积分边界条件的六阶边界值问题的可解性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-18 DOI:10.1002/mma.10492

Faouzi Haddouchi, Nourredine Houari

{"title":"具有多点和多期积分边界条件的六阶边界值问题的可解性","authors":"Faouzi Haddouchi, Nourredine Houari","doi":"10.1002/mma.10492","DOIUrl":null,"url":null,"abstract":"This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"28 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions\",\"authors\":\"Faouzi Haddouchi, Nourredine Houari\",\"doi\":\"10.1002/mma.10492\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/mma.10492\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/mma.10492","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文旨在研究涉及非局部和积分边界条件的六阶微分方程解的存在性和唯一性。首先，我们获得了相关格林函数的性质。通过应用 Krasnoselskii-Zabreiko 定点定理，我们得到了至少一个非微分解的存在性结果。此外，我们还通过荷尔德不等式、闵科夫斯基不等式和鲁斯定理确定了所考虑问题的唯一解的存在性。最后，我们还列举了两个数值示例来说明我们主要结果的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions

This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.