一类差分方程亚纯解的增长级

Growth of meromorphic solutions for some linear difference equations

主要研究了高阶线性齐次差分方程Anf(z+n)+…+A0f(z)=0亚纯解的增长级,利用Nevanlinna值分布的基本理论和复振荡理论,在假设系数Ak(k=0,1,…,n)中有一个具有有穷亏值条件时,得到了差分方程亚纯解f(z)的增长级和a值点收敛指数与系数的增长级之间的关系,推广了陈宗煊和孙光镐以及Chiang和Feng等人的结果。

In this paper,the growth of meromorphic solutions for the hmogeneous linear difference equations was investgated.By using the fundamental theorems of Nevanlinna’s value distribution theory and the complex oscillation theory,twe revealed the relationships between the growth of every meromonphic solu-tion and the growth of coefficients,and the relationship between zeros exponent of convergence of mero-monphic function and growth of coefficients,when one of coefficients had a finite deficient value,which should improve the result of Chen Zongxuan,Shon Kwangho[5]and chiang Yikman,Feng Shaoji[6].