摘要
作者讨论了起源于q-PV方程簇的一类非线性差分方程,其形式为(f(z+1)f(z)-1)(f(z)f(z-1)-1)=M(z)/N(z),其中M(z)和N(z)是两个互异的非零多项式,证明了其有穷级超越亚纯解可由其零点、1值点和极点决定.即,假设f(z)是上述方程的有穷级超越亚纯解,且与亚纯函数g(z)CM分担0,1,∞,那么可得f(z)≡g(z).另外,作者也研究了上述方程当M(z)恒等于N(z)的情形,并得到同样的结论.文中给出的例子说明了所得到两个结论的精确性.
In this paper,the authors discuss a class of nonlinear difference equations,which originated from the q-PV equation family,whose form is(f(z+1)f(z)-1)(f(z)f(z-1)-1)=M(z)/N(z),where M(z)and N(z)are two distinct non-zero polynomials.The authors prove that its transcendental meromorphic solutions with finite order can be determined by their zeros,1 value points,and poles.That is,if f(z)is a transcendental meromorphic solution with finite order of the above equation and sharing 0,1,∞CM with a meromorphic function g(z),then f(z)≡g(z).In addition,the authors also study the case of the above equation where M(z)is identical to N(z),which leads to the same conclusion.Examples for the sharpness of the two conclusions obtained are given in the paper.
作者
陈创鑫
张然然
陈宝琴
CHEN Chuangxin;ZHANG Ranran;Chen Baoqin(College of Mathematics and Data Science,Zhongkai University of Agriculture and Engineering,Guangzhou 510225,China;Corresponding author.School of Mathematics,Guangdong University of Education,Guangzhou 510303,China;Faculty of Mathematics and Computer,Guangdong Ocean University,Zhanjiang 524088,Guangdong,China)
出处
《数学年刊(A辑)》
北大核心
2025年第3期321-332,共12页
Chinese Annals of Mathematics
基金
广东省特色创新项目(No.2024KTSCX022)
国家自然科学基金(No.12101138)的资助。
关键词
非线性差分方程
亚纯函数
唯一性
Non-linear difference equations
Meromorphic function
Uniqueness
