一类势函数具有脉冲点的Sturm-Liouville算子的半逆问题

Half-inverse problem of a class of Sturm-Liouville operator with pulse points of potential function

目的研究势函数具有脉冲点的Sturm-Liouville算子在Robin边值条件下的半逆问题。方法根据缺失一个特征值后的一组谱和[0,1/2]区间上的势函数q(x)及边值条件中的参数h利用Pivovarchik的方法进行重构。结果与结论得到了(1/2,1]区间上q(x)和参数H的存在性和唯一性,给出了唯一解相应的重构算法。

Purposes—To study the half-inverse problem of Sturm-Liouville operator with impulsive point of potential function under the Robin boundary value condition.Methods—According to a set of spectrum after missing a eigenvalue,the potential function q(x)on[0,1/2]and the parameter h in the boundary condition,the method of pivotarchik is used to reconstruct the potential function.Result and Conclusion—The existence and uniqueness of q(x)on(1/2,1]and the parameter H are discussed,and the corresponding reconstruction algorithm of the unique solution is given.