On the functional-differential equation of advanced type \(f^{\prime }(x)=af(\lambda x), \lambda >1\), with \(f(0)=0\) (Q882031)
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scientific article; zbMATH DE number 5156441
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the functional-differential equation of advanced type \(f^{\prime }(x)=af(\lambda x), \lambda >1\), with \(f(0)=0\) |
scientific article; zbMATH DE number 5156441 |
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On the functional-differential equation of advanced type \(f^{\prime }(x)=af(\lambda x), \lambda >1\), with \(f(0)=0\) (English)
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23 May 2007
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The author is interested in the study of the linear functional differential equation \[ f'(x) = af(\lambda x), \quad \lambda >1, \] with the condition \( f(0) = 0.\) It seems to be simple but it is complicated to construct a solution as in ordinary or delay differential equation. In the paper the author tranforms the equation to an operator on a suitable space for which he proves the existence of a fixed point.
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advanced Functional differential equation
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Fourier transform
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