微分差分方程的亚纯解 献给余家荣教授100华诞

Meromorphic solutions of some differential-difference equations

本文研究微分差分方程f2+p(z)f(z+c)+h(z)f’(z)+g(z)=p1e^α1zn+p2^eα2zn,其中n∈N^+,c∈C\{0},α1和α2是两个不同的非零常数,方程系数为ezn的小函数.我们得到上述方程亚纯解的性质,推广并完善了前人的一些结果.

In this paper,we investigate the differential-difference equation f2(z)+p(z)f(z+c)+h(z)f’(z)+g(z)=p1^ eα1zn-p2^eα2zn,where n ∈ N^+,c ∈C\{0},α1,α2 are two distinct nonzero constants,with coefficients being small functions of ezn.We study properties of meromorphic solutions of the above equation,which have extended and improved some known results obtained recently.