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一类高阶分差分方程亚纯解的性质
引用本文:彭长文,陈宗煊. 一类高阶分差分方程亚纯解的性质[J]. 华南师范大学学报(自然科学版), 2014, 46(3): 25-0
作者姓名:彭长文  陈宗煊
作者单位:1.1.贵州师范学院 数学与计算机科学学院
基金项目:国家自然科学基金项目(11171119);贵州师范学院校级科研项目(13BS011)
摘    要:利用 亚纯函数的Nevanlinna值分布理论的差分模拟,研究了非线性高阶差分方程$ P_{1}(z)prod_{i=1}^{n}f(z+c_{i})=P_{2}(z)f(z)^{n}$亚纯解的零点,极点收敛指数和增长级,其中$n$是一个正整数,$c_i(i=1,...,n)$是非零复常数,$P_1(z),P_2(z)$是非零多项式.在给定条件下,得到了这类差分方程亚纯解的增长级的精确估计.

关 键 词:非线性差分方程
收稿时间:2013-11-28

Property of meromorphic solutions of certain high order difference equations
Peng Changwen;Chen Zongxuan. Property of meromorphic solutions of certain high order difference equations[J]. Journal of South China Normal University(Natural Science Edition), 2014, 46(3): 25-0
Authors:Peng Changwen  Chen Zongxuan
Affiliation:Peng Changwen;Chen Zongxuan;School of Mathematics and Computer Science,Guizhou Normal University;School of Mathematical Sciences,South China Normal University;
Abstract:By utilizing the difference analogue ofNevanlinna's value distribution theory of meromorphic functions, the exponents of convergence ofzeros, poles and the order of growth of meromorphic solutions of thenonlinear high order difference equation $ P_{1}(z)prod_{i=1}^{n}f(z+c_{i})=P_{2}(z)f(z)^{n}$ are studied, where $n$ is a positiveinteger, $~c_{i}(i=1,...,n)$ are non-vanishing complex constants,and$~P_{1}(z),~P_{2}(z)$ are given non-vanishing polynomials. The accurate estimate of the order of growth of meromorphic solutions tothis difference equation is attained under the given conditions.
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