Inverse Problem for Quasi-Periodic Differential Pencils with Jump Conditions Inside the Interval

2015 ◽  
Vol 10 (6) ◽  
pp. 1203-1212 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Jump Conditions ◽  
Differential Pencils

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.

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
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