On meromorphic solutions of algebraic differential equations in angular domains

Abstract

We obtain asymptotic estimates of meromorphic solutions to the differential equationP n (z, ω, ω′)=P n−1 (z, ω, ω′,...,ω (m) ) in the angular domain P={z:α ≤ arg z · ≤ β}. Here Pn(z, w, w′) is a polynomial in all variables, and of degree n with respect to w and w′; Pn−1(z, w, w′, ..., w(m)) is a polynomial in all variables, and of degree ≤n −1 with respect to w, w′, ..., w(m) In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P.