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复域差分, 差分方程与微分方程的解析性质
  • 项目名称：复域差分, 差分方程与微分方程的解析性质
  • 项目类别：面上项目
  • 批准号：10871076
  • 申请代码：A010503
  • 项目来源：国家自然科学基金
  • 研究期限：2009-01-01-2011-12-31
  • 项目负责人：陈宗煊
  • 负责人职称：教授
  • 依托单位：华南师范大学
  • 批准年度：2008
中文摘要：

近七年来，复域差分，复域差分方程理论，随值分布Nevanlinna理论的渗透，受到越来越重要的关注，成为一个热门的新方向。许多物理的模型就是差分方程。许多特殊函数的性质由某些差分方程表示，它是实域差分向复域的必然发展，也是不连续的离散方程向新的连续的差分方程的必然发展。本项目将研究复域差分，均差分的值分布问题，差分Painleve方程的解析性质。微分Painleve方程和离散Painleve方程一直是数学与物理学中的重要研究对象，差分Painleve方程是它们发展的必然趋势。还将研究与差分方程有密切关联的线性微分方程的性质。在前期工作中，我们得到一些关于差分，均差分的零点与不动点的性质；及第一，二类差分Painleve方程的一些性质；解决了Gundersen等提出的关于周期方程的次正规解问题。本项目将深化拓展差分，差分方程及微分方程的研究。

中文主题词： 复域差分，差分Painleve方程， 微分方程
成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 62
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期刊论文
On properties of meromorphic solutions for some difference equations
On difference equations relating to Gamma function
On value distribution of difference polynomials of meromorphic functions
On properties of difference polynomials
Meromorphic solutions of some q-difference equations
Oscillation theorem for higher-order linear differential equations with periodic coefficients
On growth of solutions of some second-order linear differential equations
The zeros distribution of higher order differential equations in an angular domain
Growth and zeros of meromorphic solution of some linear difference equations
Subnormal solutions of second order nonhomogeneous linear periodic differential equations
Normality criteria for families of meromorphic algebroid functions
Linear differential equations with entire coefficients of [p, q]-order in the complex plane
Composition of entire functions with finite iterated order
Subnormal solutions of second-order nonhomogeneous linear differential equations with periodic coeff
Meromorphic solutions of some difference equations
Normal criteria on the family of meromorphic functions with shared set
Relationships between entire functions and their forward differences
On the growth of solutions of a class of higher order linear differential equations
Oscillation theorems for higher order periodic linear differential equations
Some properties of solutions of periodic second order linear differential equations
On Sharing Values of Meromorphic Functions and Their Differences
Estimates for zeros of differences of meromorphic functions 亚纯函数差分的零点估计
Numbers of subnormal solutions for higher order periodic differential equations
Value distribution of meromorphic solutions of certain difference Painleve equations
On the operations of algebroid functions
On subnormal solutions of periodic differential equations
On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations
The hyper order of solutions of second order differential equations and subnormal solutions of perio
The zeros distribution of hyper solutions of higher order differential equations in angular domain
Properties of difference of meromorphic functions
Some results on difference Riccati equations
Value distribution of meromorphic soluteions of some q-difference equations
Meromorphic functions in the unit disc that share values in an angular
Differential equations with coefficients of slow growth in the unit disc
On a Conjecture Concerning Some Nonlinear Difference Equations
Meromorphic function sharing two sets with its difference operator
On meromorphic solutions of Riccati differential equations
Subnormal solutions differential equations with periodic coefficients
On a problem in complex oscillation theory of periodic higher order linear differential equations
On the meromorphic solutions of linear differential equations on the complex plane
Some properties of meromorphic solutions of q-difference equations
Properties on solutions of some q-difference equations
Growth of meromorphic solutions of some difference equations
A clunie lemma for difference and q-difference polynomials
Value distribution of meromorphic solutions of some q-difference equations
周期系数二阶齐次线性微分方程的次正规解
一类微分方程的解和小函数的关系
与其导数具有公共值的代数体函数的唯一性定理
Zeros of Entire Solutions to Complex Linear Difference Equations
某些q-差分方程亚纯解的增长性
某些差分多项式的亏量
On Properties of Finite Order Meromorphic Solutions of Certain Difference Painleve I equation
具有缺项级数系数的高阶齐次线性微分方程解的性质
单位圆內的随机亚纯函数
Value distribution of products of meromorphic functions and their differences
单位圆内的随机亚纯函数
关于孤立性定理
高阶非齐次线性微分方程解的性质
一类高阶周期系数线性微分方程解的性质
某类高阶周期线性微分方程解的性质
与线性微分多项式有一个公共值的整函数
Value Distribution of Meromorphic Solutions of Some q-Difference Equations
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