几类微分与差分方程组的亚纯解  

Meromorphic solutions of some type of system of differential and difference equations

作　　者：杨琰琰 魏文龙 黄志刚[1] YANG Yan-yan;WEI Wen-long;HUANG Zhi-gang(College of Mathematics and Physics, Suzhou University of Science and Technology,Suzhou Jiangsu 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《华东师范大学学报（自然科学版）》2018年第1期50-58,共9页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11001057);江苏省自然科学基金(BK2010234);苏州科技大学科研基金(xkq201405);苏州科技大学研究生科研创新项目(SKYCX16-001;SKYCX16-007)

摘　　要：文章考察了差分方程组亚纯解的性质,其中n≥4,p_1(z)、p_2(z)是不为零的多项式,h_1(z),h_2(z)是整函数.应用值分布理论,得到了该方程组的解是唯一的.此外,文章还讨论了满足一些特殊类微分差分方程构成的方程组存在有限级亚纯解的条件.This article investigates some properties of meromorphic solutions of the type of system of differential-difference equations of the following form f1n-p1(z)f2(z+c)=h1(z),f2n-P2(z)fl(z+c)=h2(z)where n>4,pi(z),p2(z)are non-zero polynomials,and hi(z),h2(z)are entire functions.By using Nevanlinna theorem,we have obtained the solution of above equation is unique.We also discuss the conditions for several types of system of differential-difference equations if the systems of equations actually pose meromorphic solutions of finite order.

关 键 词：NEVANLINNA理论 方程组 微分差分方程 亚纯解 

分 类 号：O157.5[理学—数学]