Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay
We study a frequently investigated class of linear difference equations Δv(n)=−p(n)v(n−k) with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considere...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/764351 |
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| author | J. Diblík I. Hlavičková |
| author_facet | J. Diblík I. Hlavičková |
| author_sort | J. Diblík |
| collection | DOAJ |
| description | We study a frequently investigated class of linear difference equations Δv(n)=−p(n)v(n−k)
with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n) is bounded above and below by certain functions. |
| format | Article |
| id | doaj-art-35f17a43fd6b4c5a8a2d2da6127f5603 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-35f17a43fd6b4c5a8a2d2da6127f56032025-02-03T01:30:07ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/764351764351Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single DelayJ. Diblík0I. Hlavičková1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech RepublicWe study a frequently investigated class of linear difference equations Δv(n)=−p(n)v(n−k) with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n) is bounded above and below by certain functions.http://dx.doi.org/10.1155/2012/764351 |
| spellingShingle | J. Diblík I. Hlavičková Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay Abstract and Applied Analysis |
| title | Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay |
| title_full | Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay |
| title_fullStr | Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay |
| title_full_unstemmed | Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay |
| title_short | Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay |
| title_sort | asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay |
| url | http://dx.doi.org/10.1155/2012/764351 |
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