Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis
We study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. The primary tools employed in this study include the a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024024 |
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| author | Ravindra Rao Jagan Mohan Jonnalagadda |
| author_facet | Ravindra Rao Jagan Mohan Jonnalagadda |
| author_sort | Ravindra Rao |
| collection | DOAJ |
| description | We study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. The primary tools employed in this study include the application of Banach's and Rus's fixed point theorems. Our theoretical results are applied to elastic beam deflections when the beam is subjected to a loading force and both ends are clamped. The existence and uniqueness of solutions to the models are guaranteed for certain classes of linear and nonlinear loading forces. |
| format | Article |
| id | doaj-art-e1d4150246914f2aa280e1045a3b2b83 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-e1d4150246914f2aa280e1045a3b2b832025-01-24T01:02:08ZengAIMS PressMathematical Modelling and Control2767-89462024-09-014329730610.3934/mmc.2024024Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysisRavindra Rao0Jagan Mohan Jonnalagadda1Department of Mathematics, Birla Institute of Technology & Science Pilani, Hyderabad, Telangana 500078, IndiaDepartment of Mathematics, Birla Institute of Technology & Science Pilani, Hyderabad, Telangana 500078, IndiaWe study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. The primary tools employed in this study include the application of Banach's and Rus's fixed point theorems. Our theoretical results are applied to elastic beam deflections when the beam is subjected to a loading force and both ends are clamped. The existence and uniqueness of solutions to the models are guaranteed for certain classes of linear and nonlinear loading forces.https://www.aimspress.com/article/doi/10.3934/mmc.2024024fourth-order boundary value problemgreen's functionfixed pointexistenceuniquenesselastic beam analysis |
| spellingShingle | Ravindra Rao Jagan Mohan Jonnalagadda Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis Mathematical Modelling and Control fourth-order boundary value problem green's function fixed point existence uniqueness elastic beam analysis |
| title | Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis |
| title_full | Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis |
| title_fullStr | Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis |
| title_full_unstemmed | Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis |
| title_short | Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis |
| title_sort | existence of a unique solution to a fourth order boundary value problem and elastic beam analysis |
| topic | fourth-order boundary value problem green's function fixed point existence uniqueness elastic beam analysis |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024024 |
| work_keys_str_mv | AT ravindrarao existenceofauniquesolutiontoafourthorderboundaryvalueproblemandelasticbeamanalysis AT jaganmohanjonnalagadda existenceofauniquesolutiontoafourthorderboundaryvalueproblemandelasticbeamanalysis |