Some properties of the solutions of third order linear ordinary differential equations (Q289709)
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scientific article; zbMATH DE number 6587825
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some properties of the solutions of third order linear ordinary differential equations |
scientific article; zbMATH DE number 6587825 |
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Some properties of the solutions of third order linear ordinary differential equations (English)
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31 May 2016
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Riccati equations
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criterion of Routh-Hurwitz
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asymptotic behavior
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non stability
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oscillation
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The author studies the equation NEWLINE\[NEWLINE\phi'''(t)+p(t)\phi''(t)+q(t)\phi'(t)+r(t)\phi(t)=0,NEWLINE\]NEWLINE where \(p(t)\), \(q(t)\) and \(r(t)\) are real and continuous functions on \([t_0,\infty)\). New results on the asymptotic behavior of the solution are obtained, including non stability, asymptotic formula and oscillation criteria. The main method is the transformation to a Riccati equation.
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