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On a method of study of algebraic differential equations. (English) Zbl 0915.30028

The author uses estimates from his earlier work [J. Lond. Math. Soc., II. Ser. 34, 534-540 (1986; Zbl 0608.30034)] and [Bull. Hong Kong Math. Soc. (to appear)] the absolute value of the derivatives of a meromorphic function \(w\) in the plane on sets of simple a-points to determine the order of \(w\) as a solution of a differential equation. In particular, conditions are given whereby \(w\) has finite order if it satisfies an equation of the form \(F_0 (z,w)(w')^m+ F_1 (z,w,w'', \dots,w^{(k)})(w')^{m-1}+\cdots +F_m(z,w,w'', \dots, w^{(k)})=0\), where the \(F_\gamma\), \(\gamma=0\), \(1,\dots,m\) are polynomials in each of the variables having a specified form.
Reviewer: L.R.Sons (DeKalb)

MSC:

30D30 Meromorphic functions of one complex variable (general theory)

Citations:

Zbl 0608.30034
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