Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions
In this paper, we give some results on the existence and multiplicity of positive solutions for a class of fourth-order multi-point boundary value problems with a sign-changing Green’s function. Using the fixed point theorem, we establish sufficient conditions for the existence of positive solutions...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/13/2093 |
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| _version_ | 1849320025911984128 |
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| author | Zhenghao Du Huijuan Zhu Fanglei Wang |
| author_facet | Zhenghao Du Huijuan Zhu Fanglei Wang |
| author_sort | Zhenghao Du |
| collection | DOAJ |
| description | In this paper, we give some results on the existence and multiplicity of positive solutions for a class of fourth-order multi-point boundary value problems with a sign-changing Green’s function. Using the fixed point theorem, we establish sufficient conditions for the existence of positive solutions in different scenarios. Finally, this article provides several specific examples to illustrate the obtained conclusions. The main innovation of this paper is to address the challenges posed by Green’s functions with changing sign, which complicate the application of standard techniques. |
| format | Article |
| id | doaj-art-52294d039ed3441eb2b051ef8bebbf21 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-52294d039ed3441eb2b051ef8bebbf212025-08-20T03:50:16ZengMDPI AGMathematics2227-73902025-06-011313209310.3390/math13132093Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary ConditionsZhenghao Du0Huijuan Zhu1Fanglei Wang2School of Mathematics, Hohai University, Nanjing 210098, ChinaSchool of Mathematics, Hohai University, Nanjing 210098, ChinaSchool of Mathematics, Hohai University, Nanjing 210098, ChinaIn this paper, we give some results on the existence and multiplicity of positive solutions for a class of fourth-order multi-point boundary value problems with a sign-changing Green’s function. Using the fixed point theorem, we establish sufficient conditions for the existence of positive solutions in different scenarios. Finally, this article provides several specific examples to illustrate the obtained conclusions. The main innovation of this paper is to address the challenges posed by Green’s functions with changing sign, which complicate the application of standard techniques.https://www.mdpi.com/2227-7390/13/13/2093multi-point boundary value problemsign-changing Green’s functionpositive solutionsfixed point theorems |
| spellingShingle | Zhenghao Du Huijuan Zhu Fanglei Wang Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions Mathematics multi-point boundary value problem sign-changing Green’s function positive solutions fixed point theorems |
| title | Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions |
| title_full | Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions |
| title_fullStr | Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions |
| title_full_unstemmed | Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions |
| title_short | Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions |
| title_sort | some results of positive solutions for a beam equation with multi point boundary conditions |
| topic | multi-point boundary value problem sign-changing Green’s function positive solutions fixed point theorems |
| url | https://www.mdpi.com/2227-7390/13/13/2093 |
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