A uniqueness theorem for indefinite Sturm-Liouville operators  

作　　者：WANG Yu-ping 

机构地区：[1]Department of Applied Mathematics,Nanjing Forestry University,Nanjing,210037,Jiangsu,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第3期345-352,共8页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11171152);the Jiangsu Natural Science Foundation of China(BK2010489)

摘　　要：In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.

关 键 词：Inverse problem uniqueness theorem indefinite Sturm-Liouville problem eigenvalue. 

分 类 号：O175.3[理学—数学] O174.52[理学—基础数学]