## 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)

Zbl 0608.30034