大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2012年
3期
53-58
,共6页
谱%势函数%半逆问题%参数边界条件
譜%勢函數%半逆問題%參數邊界條件
보%세함수%반역문제%삼수변계조건
spectrum%potential function%half-inverse problem%eigenparamenter boundary condtions
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).
Sturm-Liouville算子的半逆問題討論由一組譜和半區間上勢函數唯一確定整箇區間上勢函數q(x).本文利用Koyunbakan和Panakhov的方法和[13]的結論,討論(0,π)上的奇型Sturm-Liouville問題滿足-y″+[q(x)-1/4sin2x]y=λy,參數邊界條件y(0,λ)=0或y′(0,λ)-hy(0,λ)=0和y′(π,λ)+(aλ+b)y(π,λ)=0,證明一組譜和(π/2,π)上的勢函數q(x)唯一確定(0,π)上的勢函數q(x).
Sturm-Liouville산자적반역문제토론유일조보화반구간상세함수유일학정정개구간상세함수q(x).본문이용Koyunbakan화Panakhov적방법화[13]적결론,토론(0,π)상적기형Sturm-Liouville문제만족-y″+[q(x)-1/4sin2x]y=λy,삼수변계조건y(0,λ)=0혹y′(0,λ)-hy(0,λ)=0화y′(π,λ)+(aλ+b)y(π,λ)=0,증명일조보화(π/2,π)상적세함수q(x)유일학정(0,π)상적세함수q(x).
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)