Periodic boundary value problems for first-order impulsive difference equations with time delay
Abstract This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new comparison theorems are established. Using Schaefer’s fixed point theorem, suffici...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1539-5 |
| _version_ | 1819047468514410496 |
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| author | Jingfeng Tian Wenli Wang Wing-Sum Cheung |
| author_facet | Jingfeng Tian Wenli Wang Wing-Sum Cheung |
| author_sort | Jingfeng Tian |
| collection | DOAJ |
| description | Abstract This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new comparison theorems are established. Using Schaefer’s fixed point theorem, sufficient conditions for the existence and uniqueness of solutions to the corresponding linear problem of the boundary value problem are derived. By utilizing monotone iterative methods combined with the methods of lower and upper solutions, an existence theorem of extremal solutions to first-order impulsive difference equations with delay is obtained. These results extend some existing results in the literature. An interesting example is also given to verify the results obtained. |
| first_indexed | 2024-12-21T11:00:51Z |
| format | Article |
| id | doaj.art-44b36bdcf33443f193e93510ff509cbc |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-21T11:00:51Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-44b36bdcf33443f193e93510ff509cbc2022-12-21T19:06:21ZengSpringerOpenAdvances in Difference Equations1687-18472018-03-012018111410.1186/s13662-018-1539-5Periodic boundary value problems for first-order impulsive difference equations with time delayJingfeng Tian0Wenli Wang1Wing-Sum Cheung2College of Science and Technology, North China Electric Power UniversityDepartment of Information Engineering, China University of Geosciences Great Wall CollegeDepartment of Mathematics, University of Hong KongAbstract This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new comparison theorems are established. Using Schaefer’s fixed point theorem, sufficient conditions for the existence and uniqueness of solutions to the corresponding linear problem of the boundary value problem are derived. By utilizing monotone iterative methods combined with the methods of lower and upper solutions, an existence theorem of extremal solutions to first-order impulsive difference equations with delay is obtained. These results extend some existing results in the literature. An interesting example is also given to verify the results obtained.http://link.springer.com/article/10.1186/s13662-018-1539-5Impulsive difference equationsTime delayComparison principlePeriodic boundary value problemExtremal solutions |
| spellingShingle | Jingfeng Tian Wenli Wang Wing-Sum Cheung Periodic boundary value problems for first-order impulsive difference equations with time delay Advances in Difference Equations Impulsive difference equations Time delay Comparison principle Periodic boundary value problem Extremal solutions |
| title | Periodic boundary value problems for first-order impulsive difference equations with time delay |
| title_full | Periodic boundary value problems for first-order impulsive difference equations with time delay |
| title_fullStr | Periodic boundary value problems for first-order impulsive difference equations with time delay |
| title_full_unstemmed | Periodic boundary value problems for first-order impulsive difference equations with time delay |
| title_short | Periodic boundary value problems for first-order impulsive difference equations with time delay |
| title_sort | periodic boundary value problems for first order impulsive difference equations with time delay |
| topic | Impulsive difference equations Time delay Comparison principle Periodic boundary value problem Extremal solutions |
| url | http://link.springer.com/article/10.1186/s13662-018-1539-5 |
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