Asymptotic behavior of solutions to a class of non-autonomous delay differential equations (Q321808)
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scientific article; zbMATH DE number 6638930
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of solutions to a class of non-autonomous delay differential equations |
scientific article; zbMATH DE number 6638930 |
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Asymptotic behavior of solutions to a class of non-autonomous delay differential equations (English)
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14 October 2016
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Bernfeld-Haddock conjecture
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non-autonomous differential equation
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time-varying delay
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asymptotic behavior
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Given some continuous positive bounded functions \(\tau(t)\) and \(\gamma(t)\), and some positive odd number \(n\), the main result of the paper states that every solution of the equation NEWLINE\[NEWLINEx'(t)=\gamma(t)[-x^{\frac{1}{n}}(t)+x^{\frac{1}{n}}(t-\tau(t))]NEWLINE\]NEWLINE tends to a constant as \(t\to+\infty\), for certain initial conditions. The work concludes with some examples illustrating the results by numerical simulation and formulate open problems in this direction.
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