超越型二阶周期线性微分方程复振荡的一个结果  

A Result Concerning the Complex Oscillation for Periodic Second Order Linear Differential Equations of Transcendental Type

作　　者：高仕安[1] 

机构地区：[1]华南师范大学数学系,广东广州510631

出　　处：《应用数学》2002年第3期85-88,共4页Mathematica Applicata

基　　金：广东省自然科学基金 (980 0 15 ) ;国家自然科学基金 (199710 2 9)

摘　　要：本文证明 :设B( ζ) =g1( 1 /ζ) + g2 ( ζ) ,其中 g1(t)和 g2 (t)都是整函数 ,且至少有一是级小于 1的超越整函数 .令A(z) =B(ez) .对于方程w″+A(z)w =0的某解 f(z) 0 ,如果其零点较少 ,则 f(z)和 f(z+ 2πi)线性相关 .并且上方程的任二线性无关解至少有一零点收敛指数为无穷 .这一结论大大改进了作者先前的一个结果 .We prove:Suppose B(ζ)=g 1(1/ζ)+g 2(ζ),where g 1(t) and g 2(t) are entire functions, and at least one is transcendental with order less than 1. Set A(z)=B(e z) .For the equation w″+A(z)w=0 , if its some solution f(z) 0 is of few zeros, then f(z) and f(z+2πi) are linearly dependent. And for its arbitrary two linearly independent solutions ,at least one is of infinite exponent of convergence of zeros. This conclusion improves a previous result of the author greatly.

关 键 词：微分方程 周期 复振荡 线性相关性 

分 类 号：O174.52[理学—数学]