scholarly journals INVERSE PROBLEM OF A STURM-LIOUVILLE OPERATOR WITH NON-SEPARATED BOUNDARY VALUE CONDITIONS AND SYMMETRIC POTENTIAL

2019 ◽  
Vol 5 (327) ◽  
pp. 59-69
Author(s):  
A.Sh. Shaldanbayev ◽  
◽  
A.А. Shaldanbayeva ◽  
B.A. Shaldanbay ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Boundary Value ◽  
Symmetric Potential ◽  
Sturm Liouville

scholarly journals INVERSE PROBLEM OF STURM-LIOUVILLE OPERATOR WITH NON-SEPARATED BOUNDARY VALUE CONDITIONS AND SYMMETRIC POTENTIAL

2019 ◽  
Vol 6 (328) ◽  
pp. 52-62
Author(s):  
A.Sh. Shaldanbayev ◽  
◽  
A.A. Shaldanbayeva ◽  
A.Zh. Beisebayeva ◽  
B.A. Shaldanbay ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Boundary Value ◽  
Symmetric Potential ◽  
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.

Bounds for distance between eigenvalues of boundary value problems with retarded argument

2019 ◽  
Vol 69 (2) ◽  
pp. 399-408
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Condition ◽  
Weight Function ◽  
Boundary Value Problems ◽  
Liouville Operator ◽  
Boundary Value ◽  
Physical Parameters ◽  
Retarded Argument ◽  
Transmission Coefficients ◽  
Sturm Liouville ◽  
Special Case

Abstract In this study we are concerned with spectrum of boundary value problems with retarded argument with discontinuous weight function, two supplementary transmission conditions at the point of discontinuity, spectral and physical parameters in the boundary condition and we obtain bounds for the distance between eigenvalues. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm-Liouville problems. In the special case that ω (x) ≡ 1, the transmission coefficients γ1 = δ1, γ2 = δ2 and retarded argument Δ ≡ 0 in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

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