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.

Sturm-Liouville Problems with Discontinuities at Two Interior Points

2018 ◽  
Vol 85 (1-2) ◽  
pp. 70
Author(s):  
Hongmei Han
Keyword(s):  
Green Function ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Resolvent Operator ◽  
Asymptotic Formulas ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville ◽  
Basic Solutions ◽  
The Resolvent Operator ◽  
Interior Points

<p>In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator <em>A</em> associated with the problem, prove the operator <em>A</em> is self-adjoint in an appropriate space <em>H</em>, construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.</p>

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