Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation
We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1830248 |
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| _version_ | 1832551219655081984 |
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| author | Jia Wei Xiaoling Han Fumei Ye |
| author_facet | Jia Wei Xiaoling Han Fumei Ye |
| author_sort | Jia Wei |
| collection | DOAJ |
| description | We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β, ak,bk are T-periodic functions and akbk>0. As applications, we give some examples to illustrate the application of these theorems. |
| format | Article |
| id | doaj-art-db08e147e98a45768695c3a8b9c07fd7 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-db08e147e98a45768695c3a8b9c07fd72025-02-03T06:04:39ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1830248Existence of Periodic Solutions for a Class of Fourth-Order Difference EquationJia Wei0Xiaoling Han1Fumei Ye2School of EducationDepartment of MathematicsDepartment of MathematicsWe apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β, ak,bk are T-periodic functions and akbk>0. As applications, we give some examples to illustrate the application of these theorems.http://dx.doi.org/10.1155/2022/1830248 |
| spellingShingle | Jia Wei Xiaoling Han Fumei Ye Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation Journal of Function Spaces |
| title | Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation |
| title_full | Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation |
| title_fullStr | Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation |
| title_full_unstemmed | Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation |
| title_short | Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation |
| title_sort | existence of periodic solutions for a class of fourth order difference equation |
| url | http://dx.doi.org/10.1155/2022/1830248 |
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