在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动

Perturbation of Eigenvalue and Eigenfunction for Higher Order Ordinary Differential Equation in the Case of Boundary Perturbation Combined with Operator Perturbation

本文研究了在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动,把摄动问题A6,μ的特征值λε,μ和特征函数y6,μ（x）按两参数ε、μ的次幂展开,并且证明这些展开式当ε、μ充分小时是收敛的。

In this paper perturbation of eigenvalue and eigenfunction for higher order ordinary differential equation in the case of boundary perturbation combined with operator perturbation we considered. Eigenvalue λ_(ε,μ) and eigenfunction y_(ε,μ)(x) of perturbation problem A_(ε,μ)may be expanded by pair small parameters ε,μ,and convergence of these expresions have been proved as ε,μ sufficient small.