Determination of differential pencils with impulse from interior spectral data
Boundary Value Problems(2019)
Abstract
In this paper, we are concerned with the inverse spectral problems for differential pencils defined on [0,π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point b∈ (0,π ) in the situation of b=π /2 and b≠π /2 . For the latter, we need the knowledge of a part of the second spectrum.
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Key words
34A55, 34L05, 34L40, Differential pencil, Discontinuous condition, Inverse problem, Interior spectral data, Uniqueness theorem
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