两类费马型q-差分微分方程的整函数解  

Entire function solutions of two types of Fermat type q-difference differential equations

作　　者：范渤 丁杰 FAN Bo;DING Jie(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,Shanxi,China)

机构地区：[1]太原理工大学数学学院

出　　处：《西北师范大学学报（自然科学版）》2019年第5期11-15,20,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11601362)

摘　　要：运用Nevanlinna值分布理论和复微分方程理论,研究了2类费马型q-差分微分方程f2(qz+c)+(f(k)(z))2=1,[f(qz+c)-f(z)]2+(f(k)(z))2=1的有限级超越整函数解的存在性.在一定条件下,获得解的精确表达式.In this paper,using Nevanlinna s value distribution theory and the complex differential equations theory,the existence of finite order transcendental entire function solutions for two types of Fermat type q -difference differential equations of the following form f 2(qz+c)+(f (k)(z)) 2=1,[f(qz+c)-f(z)] 2+(f (k)(z)) 2=1 is investigated.Moreover,the precise expression of the solutions is obtained under some assumptions.

关 键 词：整函数解 费马型q-差分微分方程 Hadmard因子分解定理 有限级 

分 类 号：O174.52[理学—数学]