On Picard's theorem (Q681768)
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scientific article; zbMATH DE number 6837568
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Picard's theorem |
scientific article; zbMATH DE number 6837568 |
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On Picard's theorem (English)
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13 February 2018
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In this paper, the author gives a connection/equivalence between Picard's theorem and the characterization of entire solutions of a differential equation. He proved that let \(a(z)\) be an entire function and let \(P(z)\) be a meromorphic function in \(\mathbb C\) with at least two distinct zeros, then an entire solution of the differential equation \[ f'+a(z)P(f)=0 \] must be constant. He also proves that this result and Picard's Theorem are equivalent in the sense that one implies the other.
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Picard's theorem
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differential equation
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entire function
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meromorphic function
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