An oscillation result of higher order linear differential equation (Q2725260)
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scientific article; zbMATH DE number 1619046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An oscillation result of higher order linear differential equation |
scientific article; zbMATH DE number 1619046 |
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22 July 2002
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complex oscillation
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linear differential equation
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non-trivial solution
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An oscillation result of higher order linear differential equation (English)
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The paper studies the complex oscillation of the differential equations \(f^{(k)}+ bf'+e^z f=0\), where \(b\) is a complex constant. If the equation admits a nontrivial solution \(f(z)\) such that \(\log^+ N(r,1/f) =o(r)\), then NEWLINE\[NEWLINEf_i(z)= \exp\left(- {s\over k}-{k-1\over 2k}+ c_ie^{z/k} \right) \sum^s_{j=-r} d_je^{jz/k} i=1,2,\dots,k.NEWLINE\]
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