关于具有正规亚纯系数的高阶线性微分方程的复振荡

Oscillation on Differential Equations of Regular Meromophic Coefficients

研究了非齐次线性微分方程f(k) +Ak-1f(k-1) +… +A1f′ +A0 f=F之解的复振荡问题 ,在A0 ,A1,… ,Ak-1,F 0均为亚纯函数 ,且存在某个As 比Aj(0≤j≤k - 1,j≠s)有较大的正规增长级 ,而且对应齐次方程f(k) +Ak-1f(k-1) +… +A1f′+A0 f=0之解满足λ(1/f ) =λ(1/f )的条件下 ,得到了该方程至多除去一个例外解f0 外 ,其余所有亚纯解都满足λ(f) =λ(f) =σ(f) =∞ .

In this thesis,we investigated the oscillation of the differential equations f (k) +A k-1 f (k-1) +...+A 0f=F where A 0,A 1,...,A k-1 ,F0 are meromorphic funtions such that there's an A s has regular order of growth,σ(A j)<σ(A s),λ(1/A s)<σ(A s)(j≠s).We have proved that under certain conditions the following case holds:the meromophic solutions of the equations satisfy λ(f)=λ(f)=∞ except one at most.