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Oscillation theory of solutions of a class of higher order linear differential equations with meromorphic coefficients. (Chinese. English summary) Zbl 1340.30139

Summary: This article is devoted to studying the higher order linear differential equations \(f^{(k)}+A_{k-2}f^{(k-2)}+\cdots +A_1f'=A_0f=0\), where \(A_j(z) (j=0,1,\dots, k-2)\) are meromorphic functions with at most finitely many poles. We show that small perturbations of such equations lead to solutions whose zeros must have infinite exponent of convergence. Some results of A. Alotaibi [Result. Math. 47, No. 3–4, 165–175 (2005; Zbl 1101.34071)] are extended.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain

Citations:

Zbl 1101.34071
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