2017
Том 69
№ 9

All Issues

On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point

Mokhon'ko A. Z.

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Abstract

We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 11, pp 1793-1809.

Citation Example: Mokhon'ko A. Z. On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point // Ukr. Mat. Zh. - 2003. - 55, № 11. - pp. 1489-1502.

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