求一类微分方程特征值上、下界的数值方法

The Numerical Treatment for Calculating Upper and Lower Bounds of the Eigenvalues of a kind of differential Equation

本文首先导出了以y″+λρ(x)y=0的特征值集为其零点集的整函数ω(λ),其中ρ(x)为分段函数(每个小段为线性或零次函数),据此,给出了一个求(ρ(x)y＇)＇+λq(x)y=0的特征值上、下界的数值方法。

In this paper the author derives an entire function w(λ), whose set of zero points is equal to the set of eigenvalues of the equation y ' +λp(x)y = 0, where p(x) is a piecewise function, which is linear or constant in every piece. Thus a new method used to obtain both lower and upper bounds of eigenvalues of equation (p(x)y ) '+λq(x)y = 0 is given.