Partial inverse nodal problems for differential pencils on a star‐shaped graph

2020 ◽  
Vol 43 (15) ◽  
pp. 8841-8855
Author(s):  
Yu Ping Wang ◽  
Chung‐Tsun Shieh ◽  
Xianbiao Wei
Keyword(s):  
Partial Inverse ◽  
Inverse Nodal Problems ◽  
Shaped Graph ◽  
Differential Pencils

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions

2018 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Mixed Boundary ◽  
Constructive Method ◽  
Asymptotic Formulas ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

AbstractThe Sturm–Liouville operator on a star-shaped graph with different types of boundary conditions (Robin and Dirichlet) in different vertices is studied. Asymptotic formulas for the eigenvalues are derived and partial inverse problems are solved: we show that the potential on one edge can be uniquely determined by different parts of the spectrum if the potentials on the other edges are known. We provide a constructive method for the solution of the inverse problems, based on the Riesz basis property of some systems of vector functions.

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

scholarly journals A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph

2018 ◽  
Vol 49 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Basis Property ◽  
Singular Potentials ◽  
Main Ingredient ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph ◽  
Partial Inverse Problem ◽  
Liouville Operators

Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the potentials on the remaining edges can be constructed by fractional parts of two spectra. A uniqueness theorem is proved, and an algorithm for the constructive solution of the partial inverse problem is provided. The main ingredient of the proofs is the Riesz-basis property of specially constructed systems of functions.

scholarly journals The partial inverse nodal problem for differential pencils on a finite interval

2019 ◽  
Vol 50 (3) ◽  
pp. 307-319
Author(s):  
Y. P. Wang ◽  
Yiteng Hu ◽  
Chung-Tsun Shieh
Keyword(s):  
Finite Interval ◽  
Reconstruction Algorithm ◽  
Inverse Nodal Problem ◽  
Partial Inverse ◽  
Nodal Data ◽  
Nodal Problem ◽  
The Right ◽  
Differential Pencils

In this paper, the partial inverse nodal problem for differential pencils with real-valued coefficients on a finite interval \([0,1]\) was studied. The authors showed that the coefficients \((q_{0}(x),q_{1}(x),h,H_0)\) of the differential pencil \(L_0\) can be uniquely determined by partial nodal data on the right(or, left) arbitrary subinterval \([a,b]\) of \([0,1].\) Finally, an example was given to verify the validity of the reconstruction algorithm for this inverse nodal problem.

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