耦合边界条件下Sturm-Liouville问题特征值与特征函数的渐近式

THE ASYMPTOTIC FORMULA OF EIGENVALUES AND EIGENFUNCTIONS OF STURM-LIOUVILLE PROBLEMS UNDER COUPLED BOUNDARY CONDITIONS

本文利用刘景麟老师《常微分算子谱论》中对分离边界条件下正则Sturm-Liouville问题的研究方法(同阶无穷小的比较),研究了一般耦合边界条件下正则Sturm-Liouville问题,给出了耦合情形下的特征值与特征函数的渐近估计.(比已有的结果更精细)

In this paper,the regular Sturm-Liouville problem with coupled boundary conditions is studied,with use of the method of comparing the same order infinitesimals,proposed by Professor Liu Jinglin for studying the regular Sturm-Liouville problem with the separated boundary conditions,introduced in ＂Spectral Theory of Ordinary Differential Operators＂.The asymptotic formula of eigenvalues and eigenfunctions for the coupled cases is given.The precision of results appears to be better than of those obtained ever before.