Asymptotic Behavior of Solutions of Delayed Difference Equations
This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a mo...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/671967 |
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| _version_ | 1832567685397872640 |
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| author | J. Diblík I. Hlavičková |
| author_facet | J. Diblík I. Hlavičková |
| author_sort | J. Diblík |
| collection | DOAJ |
| description | This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations. |
| format | Article |
| id | doaj-art-c9b3416aaa5245658b33fb3fe720fb9b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9b3416aaa5245658b33fb3fe720fb9b2025-02-03T01:00:49ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/671967671967Asymptotic Behavior of Solutions of Delayed Difference EquationsJ. Diblík0I. Hlavičková1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, University of Technology, 602 00 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech RepublicThis contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations.http://dx.doi.org/10.1155/2011/671967 |
| spellingShingle | J. Diblík I. Hlavičková Asymptotic Behavior of Solutions of Delayed Difference Equations Abstract and Applied Analysis |
| title | Asymptotic Behavior of Solutions of Delayed Difference Equations |
| title_full | Asymptotic Behavior of Solutions of Delayed Difference Equations |
| title_fullStr | Asymptotic Behavior of Solutions of Delayed Difference Equations |
| title_full_unstemmed | Asymptotic Behavior of Solutions of Delayed Difference Equations |
| title_short | Asymptotic Behavior of Solutions of Delayed Difference Equations |
| title_sort | asymptotic behavior of solutions of delayed difference equations |
| url | http://dx.doi.org/10.1155/2011/671967 |
| work_keys_str_mv | AT jdiblik asymptoticbehaviorofsolutionsofdelayeddifferenceequations AT ihlavickova asymptoticbehaviorofsolutionsofdelayeddifferenceequations |