【摘要】 奇型Sturm-Liouville问题的势函数q(x)由两组谱唯一确定的,Sturm-Liouville算子的半逆问题讨论由一组谱和一半势函数唯一确定势函数q(x).本文利用Koyunbakan和Panakhov的方法,证明一组谱和(π/2,π)上的势函数q(x)唯一确定(0,π)上Sturm-Liouville方程含有奇型的1sin2x的势函数q(x).更多还原

【Abstract】 The potential q(x) of singular Sturm-Liouville operators can be uniquely determined from two spectrum.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 Koyunbakn and Panakhov’s method,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) for the Sturm-Liouville equation having singularity type 1/sin2x on(0,π).更多还原