非线性时滞微分方程解的性质  

On the properties of solutions to nonlinear delay differential equations

作　　者：孙合庆 李叶舟[1] 牛文潇 SUN He-qing;LI Ye-zhou;NIU Wen-xiao(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《高校应用数学学报（A辑）》2024年第4期439-450,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12171050,12071047);中央高校基本科研基金(500423101)。

摘　　要：设ω_(1),···,ω_(t)为互相判别的非零复常数,H_(0)(z),···,H_(t)(z)为亚纯函数.该文研究了Tumura-Cluine型非线性时滞微分方程f^(n)(z)+P(z,f)=H_(0)(z)+H_(1)(z)e^(ω1zq)+···+H_(t)(z)e^(ωtzq)亚纯解的零点分布和增长性,这里n(≥2),t,q∈N+,P(z,f)为时滞微分单项式.利用角域上指数多项式的性质,该文还考虑了上面方程整函数解Julia集的径向分布,并给出了相应极限方向测度的下界估计.Letω_(1),···,ω_(t)be distinct nonzero complex numbers,H_(0)(z),···,H_(t)(z)be meromorphic functions.In this paper,the zero distribution and growth of meromorphic solutions of the TumuraCluine type nonlinear delay differential equation f^(n)(z)+P(z,f)=H_(0)(z)+H_(1)(z)e^(ω1zq)+···+H_(t)(z)e^(ωtzq) are studied,where n(≥2),t,q∈N+and P(z,f)is a delay differential monomial.Using the properties of exponential polynomials in the angular domain,it also considers the radial distribution of Julia sets of entire solutions to the above equation,and the lower bound estimates of the measure of related limiting directions are verified.

关 键 词：时滞微分方程 增长性 零点分布 径向分布 测度 

分 类 号：O175.14[理学—数学]