一类非线性微分差分方程亚纯解的性质

基金项目:

国家自然科学基金项目

详细信息

Property of meromorphic solutions of certain nonlinear differential and difference equations

摘要: 利用值分布理论，研究了几类非线性差分方程是否有有限级的超越亚纯解的问题，还考虑了：微分差分方程 $~f^{n}(z)+M(z,f)=h(z)$ 是否存在有限级超越整函数解的问题，其中 $~n\geq3$ 是整数， $~h(z)$ 是非零的有理函数， $~M(z,f)$ 是系数为小函数的线性微分差分多项式.
- 微分差分多项式 /
- 差分多项式 /
- 微分差分方程 /
- 非线性差分方程
Abstract: By applying Nevanlinna's value distribution theory of meromorphic functions, the following problems are investigated: the existence of finite order transcendental meromorphic solutions of several kinds nonlinear difference equations, and differential-difference equations of the form $~f^{n}(z)+M(z,f)=h(z)$ , where n $(\geq3)$ is an integer, $h(z)$ is a given non-vanishing rational function, and $M(z,f)$ is a linear differential-difference polynomial with small meromorphic coefficients.
- difference-differential polynomial /
- difference polynomial /
- difference-differential equations /
- nonlinear difference equations