复域差分和差分方程的研究

基金项目:

国家自然科学基金项目

详细信息

摘要: 主要介绍了近十年来复域差分及 $q-$ 差分,差分方程及 $q-$ 差分方程研究的主要成果,其中包括亚纯函数对数导数引理的差分模拟;Clunie引理和Mohon'ko引理的差分模拟; 慢增长亚纯函数的差分, 均差分的零点, 不动点的存在性; 差分多项式的值分布性质;差分Riccati方程与差分Painlev\'{e}方程亚纯解的性质;复域 $q-$ 差分及 $q-$ 差分方程的解析性质.
- 亚纯函数值分布
Abstract: Due to the introduction of Nevanlinna theory of meromorphic functions, the researches on the complex difference , complex q-difference, difference equations and q-difference equations are developing rapidly in recent decades. Some main results on these topics in recent decades are investigated in this paper. These results include the difference analogue of the logarithmic derivative; the difference analogue of Clunie lemma;the difference counterpart of Mohon'ko lemma; the properties on the zeros, fixed-points on complex differences and divided difference of meromorphic functions with small order; the properties on the value distribution of difference polynomials, the properties on the meromorphic solutions of difference Riccati and Painlev\'{e} equations; the results on q-differences and meromorphic solutions of q-difference equations.
- Value distribution of meromorphic functions