费马型微分-差分方程解的性质  

On the properties of solutions of Fermat-type differential-difference equations

作　　者：陈寒霜 龙见仁 王玲 CHEN Hanshuang;LONG Jianren;WANG Ling(School of Mathematical Sciences,Guizhou Normal University,Guian New District 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵安新区550025

出　　处：《厦门大学学报（自然科学版）》2023年第3期463-467,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11861023,11501142);贵州省科技计划基金(黔科合平台人才[2018]5769-05号)。

摘　　要：利用Nevanlinna理论研究了费马型微分-差分方程解的存在性与增长性.讨论了费马型微分-差分方程解的存在性,发现了方程不存在有穷级超越整函数解的几个条件.此外还研究了非线性微分-差分方程解的增长性,证明了方程的整函数解增长级至少是1,推广和完善了已有结果.In this paper,the existence and the growth of solutions for Fermat differential-difference equations are studied by Nevanlinna theory.On the one hand,the existence of solutions for Fermat differential-difference equations is discussed,and several conditions are found that these equations do not secure finite order transcendental entire solutions.On the other hand,we investigate the growth of the solution of nonlinear dirrerential-dirrerence equation and prove that the growth order of the entire solution of the equation equals at least one.These results improve and extend previously-reported ones.

关 键 词：费马型微分-差分方程 存在性 增长级 整函数 

分 类 号：O174.5[理学—数学]