The complex oscillation theory of f''+Af'+Bf=F, where A, B, F{¬≡}0 are transcendental meromorphic functions

Xian-Yu Li

doi:10.2996/kmj/1138039968

Kodai Mathematical Journal

Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991

The complex oscillation theory of f''+Af'+Bf=F, where A, B, F{¬≡}0 are transcendental meromorphic functions

Xian-Yu Li

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Keywords: Non-homogeneous linear differential equation, Transcendental meromorphic function, Zero-sequence, Exponent of convergence, Order of growth

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1994 Volume 17 Issue 2 Pages 299-310

DOI https://doi.org/10.2996/kmj/1138039968

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Abstract

In this paper, we investigate the complex oscillation of the differential equation
f''+Af'+Bf=F
where A, B, F{¬≡}0 are finite order transcendental meromorphic functions. In some cases we obtain estimates of the order of growth and the exponent of convergence of the zero-sequence of solutions for above equation. Theorem 3 and Theorem 4 are the main results among the Theorems in this paper.

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