Half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter

2020 ◽  
Author(s):  
Abdullah Ergün ◽  
Rauf Amirov
Keyword(s):  
Inverse Problem ◽  
Spectral Parameter ◽  
Jump Conditions ◽  
Half Inverse Problem

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.

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