Deficiency Values for the Solutions of Differential Equations with Branching Point
We study the distribution of values of the solutions of an algebraic differential equation P(z, f, f′, . . . , f (s)) = 0 with the property that its coefficients and solutions have a branching point at infinity (e.g., a logarithmic singularity). It is proved that if a ∈ ℂ is a deficiency value of f...
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| Date: | 2014 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2190 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study the distribution of values of the solutions of an algebraic differential equation P(z, f, f′, . . . , f (s)) = 0 with the property that its coefficients and solutions have a branching point at infinity (e.g., a logarithmic singularity). It is proved that if a ∈ ℂ is a deficiency value of f and f grows faster than the coefficients, then the following identity takes place: P(z, a, 0, . . . , 0) ≡ 0, z ∈ {z : r 0 ≤ |z| |
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