两类非线性复域时滞微分方程亚纯函数解的存在性  

The existence of meromorphic solutions for two nonlinear complex delay-differential equations

作　　者：付雨欣 蒋业阳 刘康 FU Yuxin;JIANG Yeyang LIU Kang(School of Big Data Science,Jiangxi Science and Technology Normal University,Nanchang 330038,China)

机构地区：[1]江西科技师范大学大数据科学学院,江西南昌330038

出　　处：《南昌大学学报（理科版）》2024年第1期14-23,共10页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(20232BAB201007)。

摘　　要：研究了两类非线性复域时滞微分方程,f n+∑n j=1ωjf n-j(f′)j+q(z)e Q(z)f(k)(z+c)=p 1(z)eλz+p 2(z)e-λz与f n+∑n j=1ωjf n-j(f′)j+q^(z)e Q(z)f(k)(z+c)=u(z)e v(z)亚纯函数解的存在性,进而研究解存在情况下解的表示形式与增长性,其中n,k是满足n≥2,k≥0的两个正整数,c,λ≠0为常数,w j(j=1,…,n)为不全为零的常数,q(z),p i(z)(i=1,2)为非零有理函数,Q(z),v(z)为非常数多项式,q~(z),u(z)为增长级小于1的非零亚纯函数。结果推广了之前的一些结论,并给出一些例子说明这些解的存在性。This paper studied the existence of meromorphic solutions to two nonlinear complex delay-differential equations f n+∑n j=1ωjf n-j(f′)j+q(z)e Q(z)f(k)(z+c)=p 1(z)eλz+p 2(z)e-λz,and f n+∑n j=1ωjf n-j(f′)j+q^(z)e Q(z)f(k)(z+c)=u(z)e v(z),where n≥2,k≥0 are positive integers,c,λ≠0 are constants,ωj(j=1,…,n)are constants such thatωj(j=1,…,n)are not all zero,q(z),p i(z)(i=1,2)are non-vanishing rational functions,Q(z),v(z)are non-constant polynomials,q^(z),u(z)are non-vanishing meromorphic functions with order less than 1.Furthermore,investigated the form of existence and growth of the solutions.Our results improved and generalized some previous results.Some examples were given.

关 键 词：复域时滞微分方程 NEVANLINNA理论 亚纯函数解 Hadamard因子分解定理 

分 类 号：O175[理学—数学]