scholarly journals Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yalçın Güldü ◽  
Merve Arslantaş
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
Main Equation ◽  
Sturm Liouville ◽  
Discontinuity Conditions

We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

scholarly journals Inverse Spectral Problem for Integrodifferential Sturm-Liouville Operators with Discontinuity Conditions

2018 ◽  
Vol 64 (3) ◽  
pp. 427-458 ◽  
Author(s):  
S A Buterin
Keyword(s):  
Inverse Problem ◽  
Sufficient Conditions ◽  
Global Solvability ◽  
Convolution Integral ◽  
Main Equation ◽  
Convolution Integral Operator ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Discontinuity Conditions ◽  
Liouville Operators

We consider the Sturm-Liouville operator perturbed by a convolution integral operator on a finite interval with Dirichlet boundary-value conditions and discontinuity conditions in the middle of the interval. We study the inverse problem of restoration of the convolution term by the spectrum. The problem is reduced to solution of the so-called main nonlinear integral equation with a singularity. To derive and investigate this equations, we do detailed analysis of kernels of transformation operators for the integrodifferential expression under consideration. We prove the global solvability of the main equation, this implies the uniqueness of solution of the inverse problem and leads to necessary and sufficient conditions for its solvability in terms of spectrum asymptotics. The proof is constructive and gives the algorithm of solution of the inverse problem.

Inverse problems on star-type graphs: differential operators of different orders on different edges

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Vyacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Liouville Operator ◽  
Differential Operators ◽  
Compact Star ◽  
Spectral Characteristics ◽  
Weyl Function ◽  
Inverse Spectral Problems ◽  
Sturm Liouville

AbstractWe study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

Inverse problems for the impulsive Sturm–Liouville operator with jump conditions

2018 ◽  
Vol 27 (10) ◽  
pp. 1442-1450 ◽  
Author(s):  
Yasser Khalili ◽  
Nematollah Kadkhoda ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problems ◽  
Liouville Operator ◽  
Jump Conditions ◽  
Sturm Liouville

scholarly journals An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

2018 ◽  
Vol 50 (1) ◽  
pp. 71-102 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
Adjoint Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is given as a corollary of the main result.

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