Malmquist型差分-微分方程亚纯解的唯一性

On Unicity of Meromorphic Solutions to Difference-Differential Equations of Malmquist Type

应用Nevanlinna值分布理论研究一类Malmquist型差分-微分方程超级严格小于1的亚纯解的唯一性问题,证明该方程的亚纯解f完全由f的极点和f−e_(j)(j=1,2)的零点(不计重数)刻画,其中e_(1)和e_(2)为两个不相等的复数。

In this note,we consider the uniqueness problem on meromorphic solution f of hyper-order strictly less than 1 to a certain difference-differential equation of Malmquist type by using Nevanlinna theory.It is showed that the meromorphic solution f is uniquely determined by the poles of f and the zeros of f-e_(j)(counting multiplicities)for two distinct finite complex numbers e_(1)and e_(2).