参数边界条件下奇型Sturm-Liouville算子的半逆问题

摘要

Half-inverse problem for Sturm-Liouville operators consists of reconstruction of this operator by its spectrum and half of the potential.In this paper,using Koyunbakan and Panakhov’s methods and the results of ,we consider Sturm-Liouville problems on the interval（0,π） of the form -y″＋[q（x）-1/4sin2x]y=λy with boundary conditions y（0,λ）=0 or y′（0,λ）-hy（0,λ）=0 and y′（π,λ）＋（aλ＋b）y（π,λ）=0.We show that if q（x） is prescribed on（π/2,π）,then only one spectrum is sufficient to determine q（x） on the interval（0,π/2） for the Sturm-Liouville equation having singularity type 1/sin2x on（0,π）%Sturm-Liouville算子的半逆问题讨论由一组谱和半区间上势函数唯一确定整个区间上势函数q（x）.本文利用Koyunbakan和Panakhov的方法和[13]的结论,讨论（0,π）上的奇型Sturm-Liouville问题满足-y″＋[q（x）-1/4sin2x]y=λy,参数边界条件y（0,λ）=0或y′（0,λ）-hy（0,λ）=0和y′（π,λ）＋（aλ＋b）y（π,λ）=0,证明一组谱和（π/2,π）上的势函数q（x）唯一确定（0,π）上的势函数q（x）.