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Entire solutions of differential equations with finite order transcendental entire coefficients

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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.

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Authors and Affiliations

  1. Department of Mathematics, Jiangxi Normal University, 330027, Nanchang, China

    Chen Zongxuan

  2. Department of Mathematics, South China Normal University, 510631, Guangzhou, China

    Gao Shian

Authors
  1. Chen Zongxuan
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  2. Gao Shian
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Additional information

Project supported by the National Natural Science Foundation of China

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Zongxuan, C., Shian, G. Entire solutions of differential equations with finite order transcendental entire coefficients. Acta Mathematica Sinica 13, 453–464 (1997). https://doi.org/10.1007/BF02559937

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  • DOI: https://doi.org/10.1007/BF02559937

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