Sufficient conditions for a discrete spectrum in the case of a Sturm-Liouville equation with operator coefficients

1968 ◽  
Vol 2 (2) ◽  
pp. 147-152 ◽  
Author(s):  
B. M. Levitan ◽  
G. A. Suvorchenkova
Keyword(s):  
Discrete Spectrum ◽  
Liouville Equation ◽  
Sufficient Conditions ◽  
Sturm Liouville

scholarly journals Inverse problems for the Sturm–Liouville equation with a spectral parameter in the boundary condition

2017 ◽  
Author(s):  
Namig J. Guliyev
Keyword(s):  
Boundary Condition ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Necessary And Sufficient

Inverse problems of recovering the coefficients of Sturm--Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

scholarly journals Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients

2021 ◽  
Author(s):  
Aleksandr Kholkin
Keyword(s):  
Asymptotic Behavior ◽  
Differential Operator ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Sufficient Conditions ◽  
Triangular Matrix ◽  
Spectral Singularities ◽  
Matrix Potential ◽  
Triangular Operator ◽  
Sturm Liouville

In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out. The Green’s function and the resolvent for a non-self-adjoint differential operator are constructed. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For a non-self-adjoint Sturm-Liouville operator with a triangular matrix potential growing at infinity, an example of operator having spectral singularities is constructed.

scholarly journals Spectral analysis for the matrix Sturm-Liouville operator on a finite interval

2011 ◽  
Vol 42 (3) ◽  
pp. 305-327 ◽  
Author(s):  
Natalia Bondarenko
Keyword(s):  
Inverse Problem ◽  
Spectral Analysis ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
The Matrix ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability is obtained.

scholarly journals On partial fractional Sturm–Liouville equation and inclusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zohreh Zeinalabedini Charandabi ◽  
Hakimeh Mohammadi ◽  
Shahram Rezapour ◽  
Hashem Parvaneh Masiha
Keyword(s):  
Differential Equation ◽  
Liouville Equation ◽  
Existence Of Solutions ◽  
Liouville Problem ◽  
Existence Of A Solution ◽  
Contractive Mappings ◽  
Sturm Liouville

AbstractThe Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example. By using the α-ψ-multifunctions, we prove the existence of solutions for inclusion version of the partial fractional Sturm–Liouville problem. Finally by providing another example and some figures, we try to illustrate the related inclusion result.

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