Meromorphic Solutions for a Class of Differential Equations and Their Applications
- Authors: Lü W.R.1, Lü F.1, Wu L.1, Yang J.1
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Affiliations:
- China University of Petroleum
- Issue: Vol 53, No 5 (2018)
- Pages: 260-265
- Section: Differential Equations
- URL: https://journals.rcsi.science/1068-3623/article/view/228220
- DOI: https://doi.org/10.3103/S1068362318050023
- ID: 228220
Cite item
Abstract
In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn−1(f) = R(z)eα(z), where Pn−1(f) is a differential polynomial in f of degree ≤ n − 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn−1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman.
About the authors
W. R. Lü
China University of Petroleum
Author for correspondence.
Email: luwr@upc.edu.cn
China, Qindao, Shandong
F. Lü
China University of Petroleum
Email: luwr@upc.edu.cn
China, Qindao, Shandong
L. Wu
China University of Petroleum
Email: luwr@upc.edu.cn
China, Qindao, Shandong
J. Yang
China University of Petroleum
Email: luwr@upc.edu.cn
China, Qindao, Shandong