Sturm-Liouville问题的特征值与特征函数的渐近公式

Asymptotic formula for eigenvalues and eigenfunctions of Sturm-Liouville question

根据经典的分析方法,研究了边界条件依赖非线性特征参数的四阶Sturm-Liouville问题的特征值与特征函数的渐近公式。通过常微分方程的常数变易法及特征函数零点渐近估计,获得了边界条件含有非线性特征参数的特征值与特征函数的渐近公式。

According to the classical analysis method,the asymptotic formula of eigenvalues and eigenfunctions of Sturm-Liouville question with boundary conditions dependent on nonlinear eigenparameters are studied.By means of constant variation method of ordinary differential equation and asymptotic estimation of eigenfunction zero,the asymptotic formula of eigenvalues and eigenfunctions of boundary conditions with nonlinear eigenparameters are obtained.