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.
基金
Supported by the National Natural Science Foundation of China(11171152)
the Jiangsu Natural Science Foundation of China(BK2010489)