n阶复微分-差分方程的超越整函数解

Transcendental entire solutions of the n-th order complex differential-difference equations

利用Nevanlinna值分布理论,把复差分方程及微分方程结合起来,研究一类n阶复微分-差分方程w^((n))(z)^(2)+w(z+c)^(2)=Q(z),若出现有限级超越整函数解的情况.进一步推广刘曼莉和刘凯等的结论.

By using Nevanlinna value distribution theory and combining the complex difference equations with differential equations,we investigate whether a class of the n-th order complex differential-difference equations w^((n))(z)^(2)+w(z+c)^(2)=Q(z)have transcendental entire solutions with finite order or not.Our result extends and improves the results due to LIU Manli and LIU Kai et al.