Inverse spectral problems for differential pencils with boundary conditions dependent on the spectral parameter

2016 ◽  
Vol 40 (8) ◽  
pp. 3190-3196 ◽  
Author(s):  
Yu Ping Wang ◽  
V.A. Yurko
Keyword(s):  
Boundary Conditions ◽  
Spectral Parameter ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 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 $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

Inverse spectral problems for differential operators with non-separated boundary conditions

2020 ◽  
Vol 28 (4) ◽  
pp. 567-616
Author(s):  
Vjacheslav A. Yurko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Short Review ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Separated Boundary Conditions ◽  
Inverse Spectral ◽  
Type Boundary

AbstractWe give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.

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