Asymptotics of eigenvalues and eigenfunctions of the Sturm-Liouville problem with a small parameter and the spectral parameter in the boundary condition

1996 ◽  
Vol 60 (4) ◽  
pp. 456-458 ◽  
Author(s):  
Ben Amara Zhamel
Keyword(s):  
Boundary Condition ◽  
Small Parameter ◽  
Spectral Parameter ◽  
Liouville Problem ◽  
Asymptotics Of Eigenvalues ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville

scholarly journals Spectral Analysis of -Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Aytekin Eryılmaz
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Difference Operator ◽  
Boundary Value ◽  
Liouville Problem ◽  
Scattering Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Sturm Liouville ◽  
Spectral Representations

This paper is concerned with -Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition. We construct a self-adjoint dilation of the maximal dissipative -difference operator and its incoming and outcoming spectral representations, which make it possible to determine the scattering matrix of the dilation. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of operator generated by boundary value problem.

scholarly journals ON THE EXPANSION FORMULA FOR A SINGULAR STURM-LIOUVILLE OPERATOR

2021 ◽  
Vol 21 (1) ◽  
pp. 67-76
Author(s):  
ULVIYE DEMIRBILEK ◽  
KHANLAR R. MAMEDOV
Keyword(s):  
Boundary Condition ◽  
Green Function ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Resolvent Operator ◽  
Liouville Problem ◽  
Scattering Data ◽  
Expansion Formula ◽  
Sturm Liouville

In this study, on the semi-axis, Sturm - Liouville problem under boundary condition depending on spectral parameter is considered. In what follows scattering data is defined and its properties are given for the problem. The kernel of resolvent operator which is Green function is constructed. Using Titchmarsh method, expansion is obtained according to eigenfunctions and expansion formula is expressed with the scattering data.

scholarly journals A Sturm-Liouville Problem with a Discontinuous Coefficient and Containing an Eigenparameter in the Boundary Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Condition ◽  
Green Function ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Fundamental Solutions ◽  
Asymptotic Formulas ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville ◽  
Interior Points

We study a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We give an operator-theoretic formulation, construct fundamental solutions, investigate some properties of the eigenvalues and corresponding eigenfunctions of the discontinuous Sturm-Liouville problem and then obtain asymptotic formulas for the eigenvalues and eigenfunctions and find Green function of the discontinuous Sturm-Liouville problem.

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