复线性微分方程解的增长性的几个结果  

SOME RESULTS ON THE GROWTH OF SOLUTIONS OF COMPLEX LINEAR DIFFERENTIAL EQUATIONS

作　　者：龙见仁[1,2] LONG Jian-ren(School of Computer Science; School of Science, Beijing University of Posts and Telecommunications,Beijing 100876, China;School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China)

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

出　　处：《数学杂志》2017年第4期781-791,共11页Journal of Mathematics

基　　金：国家自然科学基金资助(11501142);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

摘　　要：本文研究了复线性微分方程解的增长性问题.利用两类具有某种渐进增长性质的函数作为线性微分方程的系数,讨论了两类二阶线性微分方程解的增长性,获得了方程解为无穷级.这些结果推广了先前的一些结果.In this paper,we study the growth problem of solutions of two classes of second order linear differential equations.By assuming their coe±cients which have the properties of asymptotic growth,we obtain that all nontrivial solutions are of infinite order,which improves and extends previous results.

关 键 词：复微分方程 整函数 无穷级 下级 渐进增长 

分 类 号：O174.5[理学—数学]