In this paper, we prove some uniqueness theorems for the solution of inverse spectral problems of Sturm-Liouville operators with boundary conditions depending linearly on the spectral parameter and with a finite number of transmission conditions.
The purpose of this paper is to solve the inverse spectral problems for Sturm-Liouville operator with boundary conditions depending on spectral parameter and double discontinuities inside the interval. It is proven that the coefficients of the problem can be uniquely determined by either Weyl function or given two different spectral sequences.
The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl's methods we show that if p (x) and q(x) are known on the interval (π/2, π), then only one spectrum suffices to determine p (x) , q(x) functions and β, h coefficients on the interval (0, π) for impulsive diffusion operator with discontinuous coefficient.
The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if q(x) is prescribed on 0, π 2 , then only one spectrum is sufficient to determine q(x) on the interval (0, π) for this problem
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