Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (2): 556-564.doi: 10.1016/S0252-9602(13)60019-3

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ON ZEROS OF SOLUTIONS OF HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS

 LAN Shuang-Ting, CHEN Zong-Xuan   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2011-10-02 Revised:2012-06-28 Online:2013-03-20 Published:2013-03-20
  • Supported by:

    This project was supported by the National Natural Science Foundation of China (11171119) and Funding of Tianyuan (11226090).

Abstract:

In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak−1 is the dominant coefficient, then every transcendental solution f(z) of equation
f(k) + Ak−1f(k−1) + … + A0f = 0
satisfies λ(f) = 1, where λ(f) denotes the exponent of convergence of zeros of the meromor-phic function f(z).

Key words: Differential equation, exponent of convergence of zeros, type

CLC Number: 

  • 30D35
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