Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives
Abstract This article addresses the existence and uniqueness of solution for fully fourth-order differential equations modeling beams on elastic foundations with nonlinear boundary conditions. The proof will rely on Perov’s fixed point theorem in complete generalized metric spaces to overcome the pr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02907-9 |
| _version_ | 1828034950599802880 |
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| author | Huiling Chen Yujun Cui |
| author_facet | Huiling Chen Yujun Cui |
| author_sort | Huiling Chen |
| collection | DOAJ |
| description | Abstract This article addresses the existence and uniqueness of solution for fully fourth-order differential equations modeling beams on elastic foundations with nonlinear boundary conditions. The proof will rely on Perov’s fixed point theorem in complete generalized metric spaces to overcome the problems due to the presence of all lower-order derivatives in the nonlinearity. Finally, some illustrating examples of the theory are presented. |
| first_indexed | 2024-04-10T15:40:41Z |
| format | Article |
| id | doaj.art-26a40b0024e6461ca7860c0a8fab4fa0 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-10T15:40:41Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-26a40b0024e6461ca7860c0a8fab4fa02023-02-12T12:25:45ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-02-012023111310.1186/s13660-022-02907-9Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivativesHuiling Chen0Yujun Cui1College of Electrical Engineering and Automation, Shandong University of Science and TechnologyCollege of Mathematics and Systems Science, Shandong University of Science and TechnologyAbstract This article addresses the existence and uniqueness of solution for fully fourth-order differential equations modeling beams on elastic foundations with nonlinear boundary conditions. The proof will rely on Perov’s fixed point theorem in complete generalized metric spaces to overcome the problems due to the presence of all lower-order derivatives in the nonlinearity. Finally, some illustrating examples of the theory are presented.https://doi.org/10.1186/s13660-022-02907-9Fully fourth-order differential equationExistence and uniquenessPerov’s fixed point theorem |
| spellingShingle | Huiling Chen Yujun Cui Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives Journal of Inequalities and Applications Fully fourth-order differential equation Existence and uniqueness Perov’s fixed point theorem |
| title | Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives |
| title_full | Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives |
| title_fullStr | Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives |
| title_full_unstemmed | Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives |
| title_short | Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives |
| title_sort | existence and uniqueness of solutions to the nonlinear boundary value problem for fourth order differential equations with all derivatives |
| topic | Fully fourth-order differential equation Existence and uniqueness Perov’s fixed point theorem |
| url | https://doi.org/10.1186/s13660-022-02907-9 |
| work_keys_str_mv | AT huilingchen existenceanduniquenessofsolutionstothenonlinearboundaryvalueproblemforfourthorderdifferentialequationswithallderivatives AT yujuncui existenceanduniquenessofsolutionstothenonlinearboundaryvalueproblemforfourthorderdifferentialequationswithallderivatives |