一类二阶线性微分方程解的增长性  

On the Growth of Solutions to Some Second Order Linear Differential Equations

作　　者：范水平[1] 陈宗煊[1] FAN Shuiping CHEN Zongxuan(School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China Corresponding author. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China.)

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《数学年刊（A辑）》2016年第1期31-40,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11171119);广东省自然科学基金项目(No.2014A030313422)的资助

摘　　要：本文研究一类二阶齐次线性微分方程f"+A_1(z)e^(P(z))f'+A_0(z)e^(Q(z))f=0,解的增长性,其中P(z)=az^n,Q(z)=bz^n,ab≠0,a=cb(c>1),A_j(z)(j=0,1)是非零多项式,证明了该方程的每个非零解满足σ(f)=∞并且σ_2(f)=n.The authors investigate the growth of solutions to some second-order differential equations f＂＋A_1（z）e^（P（z））f＇＋A_0（z）e^（Q（z））f=0,where P（z）=az^n,Q（z）=bz^n,ab≠0,a=cb（c〉1）,and A_j（z）（j=0,1） are non-zero polynomials. It is obtained that every non-zero solution $f$ of the above equation satisfies σ（f）=∞并且σ_2（f）=n

关 键 词：微分方程 整函数 超级 

分 类 号：O174.52[理学—数学] O175[理学—基础数学]