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Entire solutions of differential equations with finite order transcendental entire coefficients

Authors:

Affiliation:

(1) Department of Mathematics, Jiangxi Normal University, 330027 Nanchang, China;(2) Department of Mathematics, South China Normal University, 510631 Guangzhou, China

Abstract:

In this paper, we investigate the complex oscillation of the differential equation

$f^{left( k right)} + A_{k - 1} f^{left( {k - 1} right)} + cdots + A_0 f = F$

whereA _k−1, …,A ₀, F # 0 are finite order transcendental entire functions, such that there exists anA _d(0≤d≤k−1) being dominant in the sense that either it has larger order than any otherA _j(j=0.…,d−1, d+1.…, k−1), or it is the only transcendental function We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation. Project supported by the National Natural Science Foundation of China

Keywords:

Non-homogeneous linear differential equation Transcendental entire function Zerosequence Exponent of convergence Order of growth

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