Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays
The asymptotic behavior of the solutions of the first-order differential equation ẏ(t)=∑i=1nβi(t)[y(t-δi)-y(t-τi)] containing delays is studied with βi:[t0-τ,∞)→[0,∞), <...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/749852 |
| _version_ | 1818199274953900032 |
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| author | Josef Dibl&#237;k Miroslava R&#367;&#382;i&#269;kov&#225; Zuzana &#352;ut&#225; |
| author_facet | Josef Dibl&#237;k Miroslava R&#367;&#382;i&#269;kov&#225; Zuzana &#352;ut&#225; |
| author_sort | Josef Dibl&#237;k |
| collection | DOAJ |
| description | The asymptotic behavior of the solutions of the first-order differential equation ẏ(t)=∑i=1nβi(t)[y(t-δi)-y(t-τi)] containing delays is studied with βi:[t0-τ,∞)→[0,∞), τ=max⁡{τ1,…,τn}, ∑i=1nβi(t)>0, τi>δi>0. The attention is focused on an analysis of the asymptotical convergence of solutions. A criterion for the asymptotical convergence of all solutions, characterized by the existence of a strictly increasing bounded solution, is proved. Relationships with the previous results are discussed, too. |
| first_indexed | 2024-12-12T02:19:10Z |
| format | Article |
| id | doaj.art-4851a5844edc4fc3a2367b5557d8cf41 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T02:19:10Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4851a5844edc4fc3a2367b5557d8cf412022-12-22T00:41:44ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/749852Asymptotical Convergence of the Solutions of a Linear Differential Equation with DelaysJosef Dibl&#237;kMiroslava R&#367;&#382;i&#269;kov&#225;Zuzana &#352;ut&#225;The asymptotic behavior of the solutions of the first-order differential equation ẏ(t)=∑i=1nβi(t)[y(t-δi)-y(t-τi)] containing delays is studied with βi:[t0-τ,∞)→[0,∞), τ=max⁡{τ1,…,τn}, ∑i=1nβi(t)>0, τi>δi>0. The attention is focused on an analysis of the asymptotical convergence of solutions. A criterion for the asymptotical convergence of all solutions, characterized by the existence of a strictly increasing bounded solution, is proved. Relationships with the previous results are discussed, too.http://dx.doi.org/10.1155/2010/749852 |
| spellingShingle | Josef Dibl&#237;k Miroslava R&#367;&#382;i&#269;kov&#225; Zuzana &#352;ut&#225; Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays Advances in Difference Equations |
| title | Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays |
| title_full | Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays |
| title_fullStr | Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays |
| title_full_unstemmed | Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays |
| title_short | Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays |
| title_sort | asymptotical convergence of the solutions of a linear differential equation with delays |
| url | http://dx.doi.org/10.1155/2010/749852 |
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