Spectral properties of the general Sturm-Liouville equation with random coefficients I

1982 ◽  
Vol 109 (1) ◽  
pp. 57-78 ◽  
Author(s):  
S. A. Molčanov ◽  
H. Seidel
Keyword(s):  
Liouville Equation ◽  
Spectral Properties ◽  
Random Coefficients ◽  
Sturm Liouville

Sturm-Liouville operators with an indefinite weight function

1977 ◽  
Vol 78 (1-2) ◽  
pp. 161-191 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Scalar Product ◽  
Main Tool ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Sturm Liouville ◽  
Liouville Operators

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.

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 Transmission problem for the Sturm-Liouville equation involving a retarded argument

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2071-2080
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Discontinuous Boundary ◽  
Sturm Liouville

In this work, spectral properties of a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary conditions and in the transmission conditions at the point of discontinuity are investigated. To this aim, asymptotic formulas for the eigenvalues and eigenfunctions are obtained.

scholarly journals Some properties of eigenvalues and generalized eigenvectors of one boundary value problem

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 911-920 ◽  
Author(s):  
Hayati Olğar ◽  
Oktay Mukhtarov ◽  
Kadriye Aydemir
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problem ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Boundary Value ◽  
Discontinuous Boundary ◽  
Generalized Eigenvectors ◽  
Continuous Potential ◽  
Sturm Liouville ◽  
Piecewise Continuous

We investigate a discontinuous boundary value problem which consists of a Sturm-Liouville equation with piecewise continuous potential together with eigenparameter dependent boundary conditions and supplementary transmission conditions. We establish some spectral properties of the considered problem. In particular, it is shown that the problem under consideration has precisely denumerable many eigenvalues ?1, ?2,..., which are real and tends to +?. Moreover, it is proven that the generalized eigenvectors form a Riesz basis of the adequate Hilbert space.

scholarly journals A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sertac Goktas
Keyword(s):  
Liouville Equation ◽  
Spectral Properties ◽  
Liouville Problem ◽  
Mathematical Physics ◽  
Asymptotic Estimates ◽  
One Dimensional ◽  
Multiplicative Calculus ◽  
New Type ◽  
Sturm Liouville ◽  
The One

In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some algebraic structures. Then, some asymptotic estimates for eigenfunctions of the multiplicative Sturm-Liouville problem are obtained by some techniques. Finally, some basic spectral properties of this multiplicative problem are examined in detail.

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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