Meromorphic solutions of delay differential equations related to logistic type and generalizations
Meromorphic solutions of delay differential equations related to logistic type and generalizations
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与逻辑类型和泛化相关的时滞微分方程的亚纯解
DOI：
10.1016/j.bulsci.2021.103040
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发表时间：
2018-12
影响因子：
1.3
通讯作者：
Cao Tingbin
中科院分区：
文献类型：
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作者：
Xu Ling;Cao Tingbin
Abstract Let {b j} j= 1 k be meromorphic functions, and let w be admissible meromorphic solutions of delay differential equation w′(z)= w (z)[P (z, w (z)) Q (z, w (z))+∑ j= 1 k b j (z) w (z− c j)] with distinct delays c 1,…, c k∈ C∖{0}, where the two nonzero polynomials P (z, w (z)) and Q (z, w (z)) in w with meromorphic coefficients are prime each other. We obtain that if lim sup r→∞ log T (r, w) r= 0, then deg w(P/Q)≤ k+ 2. Furthermore, if Q (z, w (z)) has at least one nonzero root, then deg w(P)= deg w(Q)+ 1≤ k+ 2; if all roots of Q (z, w (z)) are nonzero, then deg w(P)= deg w(Q)+ 1≤ k+ 1; if deg w(Q)= 0, then deg w(P)≤ 1. In particular, whenever deg w(Q)= 0 and deg w(P)≤ 1 and without the growth condition, any admissible meromorphic solution of the above delay differential equation (called Lenhart-Travis' type logistic delay differential equation) with reduced form can not be an entire function w satisfying N‾(r, 1 w)= O (N (r, 1 w)); while if all coefficients are rational functions, then the condition N‾(r, 1 w)= O (N (r, 1 w)) can be omitted. Furthermore, any admissible meromorphic solution of the logistic delay differential equation (that is, for the simplest special case where k= 1 and deg w(P/Q)= 0) satisfies that N (r, w) and T (r, w) have the same growth category. Some examples support our results.
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影响因子：
2.2
作者：
Liu Kai;Song Chang Jiang
通讯作者：
Song Chang Jiang
线性和非线性差分方程亚纯解的增长、零点和极点
DOI：
10.1007/s11425-011-4265-y
发表时间：
2011-07
期刊：
Science China Mathematics
影响因子：
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作者：
通讯作者：
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伽马函数差分方程亚纯解的性质
影响因子：
1.3
作者：
Chen, Zong-Xuan
通讯作者：
Chen, Zong-Xuan
DOI：
10.1090/s0002-9939-1986-0813814-3
发表时间：
1986
期刊：
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影响因子：
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作者：
S. Lenhart;C. Travis
通讯作者：
S. Lenhart;C. Travis
DOI：
10.1007/978-1-4419-7646-8
发表时间：
2011-01-01
期刊：
INTRODUCTION TO DELAY DIFFERENTIAL EQUATIONS WITH APPLICATIONS TO THE LIFE SCIENCES
影响因子：
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作者：
Smith, Hal
通讯作者：
Smith, Hal