非线性微分-差分方程的解  

SOLUTIONS OF NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

作　　者：张石梅 龙见仁 吴秀碧[1,3] ZHANG Shi-mei;LONG Jian-ren;WU Xiu-bi(School of Mathematical Science,Guizhou Normal University,Guiyang 550001,China;School of Computer Science;School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China;School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550001 [2]北京邮电大学计算机学院理学院,北京100876 [3]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《数学杂志》2018年第6期1107-1118,共12页Journal of Mathematics

基　　金：国家自然科学基金资助(11501142;11601100);贵州省科学技术基金资助(黔科合J字[2015]2112号);贵州师范大学2016年博士科研启动项目资助;2016年度贵州省"千"层次创新型人才项目资助

摘　　要：本文研究了非线性微分-差分方程f(z)~n+a_(n-1)f(z)^(n-1)+…+a_1f(z)+q(z)e^(Q(z))f^((k))(z+c)=P(z)的有穷级非零整函数解的增长性和零点分布问题.利用微分-差分Nevanlinna值分布的方法,获得了当方程的系数满足一定条件时,方程解的增长性估计和零点分类.特别地,当n=2, a_1≠0指数多项式解满足某些条件时,获得了解具有特别的形式.该结果推广了先前文献[1,2]的结果.In this paper,we study the growth and distribution of zeros of entire solutions ofˉnite order of nonlinear differential-difference equation f(z)n+an-1f(z)n-1+...+a1f(z)+q(z)eQ(z)f(k)(z+c)=P(z):By using the differential-difference Nevanlinna values distribution theory,we obtain an estimation of the growth and the distribution of zeros of solutions of the differential-difference equation if there are some attached condiction on the coe±cients.Particularly,when n=2 and a1≠0,we obtain that exponential polynomial solutions satisfying some condictions must reduce to rather specific forms,which improves the results of[1,2].

关 键 词：微分-差分方程 指数多项式 有穷级 

分 类 号：O174.5[理学—数学]