二阶线性微分方程复振荡的若干结果  

Some Complex Oscillation Results of Solutions of Second-Order Linear DifferentialEqtiations

作　　者：袁文俊[1] 

机构地区：[1]伊犁师范学院数学系

出　　处：《数学学报（中文版）》1995年第1期45-50,共6页Acta Mathematica Sinica：Chinese Series

基　　金：新疆教委高校科研资助课题

摘　　要：本文给出了方程（１１）具有一个（或两个线性无关）解其零点收敛指数小于（或不小于）Ａ（ｚ）的增长级的必要条件（或充分条件）．我们得到了４个定理并且推广了Ｉ．Ｌａｉｎｅ的两个结果，我们还证明了如果Ａ（ｚ）是无穷级的整函数，则方程（１．１）的任两线性无关解或者无零点或者至少有一解其零点收敛指数为无穷．We give essential(or sufficient)conditions on A(z)that the equation y'+A(z)y=0possess one(or two linearly independent)solution with the exponent of convergence of its zerosless(or no less)than the growth orderof A(z).We obtain four theorems and generalize tworesults of I. Laine. We also prove tliat if A(z)is an entire of infinite order,then any two linearlyindependent solutions of y'+A(z)y=0 have no zeros unless the maximum value of the exponentsof convergence of their zeros is infinite.

关 键 词：复振荡 收敛指数 解 微分方程 线性 

分 类 号：O175.1[理学—数学]