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 |
| Summary: | 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. |
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| ISSN: | 1687-1839 1687-1847 |