非线性微分方程和差分方程的研究

In this proposal, we will research the existences of global solutions of nonlinear differential equations and try to find out all or some global solutions of some nonlinear differential equations. We will research the properties of meromorphic and entire solutions of nonlinear differential equations and reduce some nonlinear differential equations with admissible solutions to some standard forms. At the same time, we will study the existences and properties of meromorphic and entire solutions of difference equations, the simplifications of the nonlinear difference equations, relationship between the special functions and difference or differential equations. We will study the dynamical properties of the meromorphic and entire solutions of nonlinear differential and difference equations. We will also research uniqueness of the meromorphic and entire solutions of nonlinear differential and difference equations and other relative topics.

我们将研究非线性微分方程整体解的存在性并寻找一些非线性微分方程的全部或部分整体解，我们将研究非线性微分方程亚纯函数解和整函数解的性质，具有允许解的非线性微分方程的简化。同时，我们也将研究差分方程亚纯函数解和整函数解的存在性以及相关性质，我们将研究非线性差分方程的简化问题，特殊函数与差分方程和微分方程的联系。我们还将研究非线性微分方程和差分方程亚纯函数解和整函数解的动力学性质，唯一性问题以及相关的研究课题。

在本项目中，我们研究了几类非线性微分方程亚纯解的存在性和解的结构；非线性微分方程在值分布理论中的应用。我们研究了一些差分方程亚纯解的性质，涉及差分算子的亚纯函数的唯一性。我们还研究了一些有理函数和超越亚纯函数的复动力系统性质，一类偏微分方程整体强解的性质。