In this paper, we consider the inverse spectral problem for the impulsive Sturm-Liouville differential pencils on [0, π] with the Robin boundary conditions and the jump conditions at the point 2. We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials given on where is the spectral parameter, p(x) ∈ W 1 2 [0, ], q(x) ∈ L 2 [0, ] are real-valued functions, is a real number, and > 0, ≠ 1. Here we denote by W m 2 [0, ] the space of functions f (x), x ∈ [0, ], such

No abstract

In this study, the diffusion operator with discontinuity function and the jump conditions is considered. Under certain initial and discontinuity conditions, integral equations have been derived for the solutions. Integral representations, which is too useful for this type equation, have been presented.

No abstract

In this paper, half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter is considered. The half inverse problems is studied of determining the coefficient and potential functions of the value problem from its spectrum by using the Yang-Zettl and Hocstadt-Lieberman methods. We show that if the functions p(x) and q(x) are prescribed over the semi-interval, then potential functions are determined uniquely by one spectrum on the over interval.