On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients

Jianren Long, Chunhui Qiu and Pengcheng Wu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We consider that the linear differential equations f(k) + Ak−1(z)f(k−1) + ⋯+A1(z)f′ + A0(z)f = 0, where Aj (j = 0,1, …, k − 1), are entire functions. Assume that there exists l ∈ {1,2, …, k − 1}, such that Al is extremal for Yang′s inequality; then we will give some conditions on other coefficients which can guarantee that every solution f(≢0) of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of f if every solution f(≢0) of the equation is of infinite order.

Date: 2014
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https://doi.org/10.1155/2014/305710

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:305710

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