有限增长级条件下超越整函数和亚纯函数的一阶差分方程的零点和不动点研究  

Zero and Fixed Points of First-order Difference Equation with Finite Order

作　　者：章辉梁 高宗升[1] 

机构地区：[1]北京航空航天大学数学信息与行为教育部重点实验室,北京100191

出　　处：《长江大学学报（自科版）（上旬）》2016年第2期10-13,3,共4页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目(11371225)

摘　　要：对超越整函数和亚纯函数一阶差分方程的零点和不动点的研究,很多的研究结果都是基于函数的增长级σ(f)≤1,而在有限增长级1<σ(f)<∞的情况下,研究结果则相对较少。利用Nevanlinna的基本理论和方法,探讨了在有限增长级的条件下,超越整函数和亚纯函数一阶差分方程零点和不动点的存在性。首先,结合Hadmard因子分解定理研究了在一定的条件下超越整函数的一阶差分方程零点和不动点的存在性,证明了其有无穷多个零点和无穷多个不动点。其次,把对超越整函数的零点和不动点的存在性研究,推广到了亚纯函数,继续探讨了亚纯函数在有限增长级条件下零点和不动点的情况,得出了相应的结论。Many results concerning the existence of zero and fixed points of first-order difference equation is based on the case that its order is less than or equal to 1,while few conclusions are obtained when its order is finite.Some results concerning the existence of zero and fixed points of first-order difference equation are obtained when order of function is finite by using the basic theory of Nevanlinna.First,the existence of zero and fixed points of entire function is studied by applying factorization theorem of Hadmard,it proves that first-order difference equation of entire function has infinitely many zero and fixed points.Second,the case is extended to meromorphic function and some similar results are obtained when the order of meromorphic function is finite.

关 键 词：一阶差分 零点 不动点 

分 类 号：O174.5[理学—数学]