scholarly journals Determination of differential pencils with spectral parameter dependent boundary conditions from interior spectral data

2013 ◽  
Vol 37 (6) ◽  
pp. 860-869 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Xiu-Juan Yu
Keyword(s):  
Boundary Conditions ◽  
Spectral Data ◽  
Spectral Parameter ◽  
Differential Pencils ◽  
Parameter Dependent

scholarly journals On half inverse problem for differential pencils with the spectral parameter in boundary conditions

2011 ◽  
Vol 42 (3) ◽  
pp. 355-364 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Finite Interval ◽  
A Priori ◽  
Half Inverse Problem ◽  
Differential Pencils ◽  
Parameter Dependent ◽  
The Uniqueness Theorem

A second-order differential pencil on a finite interval with spectral parameter dependent boundary conditions is considered. The inverse problem is studied of recovering the coefficients of the boundary value problem from its spectrum, provided that on one half of the interval they are known a priori. The uniqueness theorem for this inverse problem is proved and a constructive procedure for finding its solution is obtained.

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.

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