scholarly journals The inverse problem for differential pencils with eigenparameter dependent boundary conditions from interior spectral data

2012 ◽  
Vol 25 (7) ◽  
pp. 1061-1067 ◽  
Author(s):  
Yu Ping Wang
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Data ◽  
Differential Pencils

The inverse problem for differential pencils on a star-shaped graph with mixed spectral data

2020 ◽  
Vol 63 (8) ◽  
pp. 1559-1570 ◽  
Author(s):  
Yu Ping Wang ◽  
Natalia Bondarenko ◽  
Chung Tsun Shieh
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Shaped Graph ◽  
Differential Pencils

An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
Chinare G. Ibadzadeh ◽  
Ibrahim M. Nabiev
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Spectral Data ◽  
Spectral Parameter ◽  
Boundary Value ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

AbstractIn this paper a boundary value problem is considered generated by the Sturm–Liouville equation and non-separated boundary conditions, one of which contains a spectral parameter. We give a uniqueness theorem, develop an algorithm for solving the inverse problem of reconstruction of boundary value problems with spectral data. We use the spectra of two boundary value problems and some sequence of signs as a spectral data.

A uniqueness result for differential pencils with discontinuities from interior spectral data

Analysis ◽  
2019 ◽  
Vol 38 (4) ◽  
pp. 195-202
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Uniqueness Result ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Differential Pencils

Abstract In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions {q_{0}(x)} and {q_{1}(x)} applied in the diffusion operator.

scholarly journals Recovering differential pencils with spectral boundary conditions and spectral jump conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Second Order ◽  
Uniqueness Theorems ◽  
Jump Conditions ◽  
Internal Point ◽  
Differential Pencils

AbstractIn this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: $(i)$ ( i ) the potentials $q_{k}(x)$ q k ( x ) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point $b\in (\frac{\pi }{2},\pi )$ b ∈ ( π 2 , π ) and parts of two spectra; $(ii)$ ( i i ) if one boundary condition and the potentials $q_{k}(x)$ q k ( x ) are prescribed on the interval $[\pi /2(1-\alpha ),\pi ]$ [ π / 2 ( 1 − α ) , π ] for some $\alpha \in (0, 1)$ α ∈ ( 0 , 1 ) , then parts of spectra $S\subseteq \sigma (L)$ S ⊆ σ ( L ) are enough to determine the potentials $q_{k}(x)$ q k ( x ) on the whole interval $[0, \pi ]$ [ 0 , π ] and another boundary condition.

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.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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.

Sign in / Sign up

Export Citation Format

Share Document