一种不规范的斯特姆-刘维本征值问题

由于端点系有集中质量的弹性杆的振动问题的边界条件不是斯特姆－刘维本征值问题所要求的边界条件，分离变数所得到的函数系{Xn(x)}不是正交函数系，故求解十分困难，本文提出一种变换，将其边界条件化为第一类，第二类或第三类边界条件，此时{Xn(x)}为正交完备函数系，问题大为简化，最后给出了几种不同端点情况下此类问题的解。

One question on the irregular Sturm-Liouville eigenvalue problem

It's very difficult to solve the oscillation problem of elastic rod with concentrated mass on the end because the boundary condition in this case is not the one required by Sturm Liouville eigenvalue problem and the functions{X n(x)} are not orthogonal ones.This problem is simplified by presenting a transformation,with which the boundary condition is changed to the boundary condition of first ,second or third class and then the functions {X n(x)}are orthogonal complete functions.Some solutions to such problems with different ends are discussed .