scholarly journals Inverse Sturm-Liouville problem with a boundary condition linear in the spectral parameter

2018 ◽  
Vol 2018 ◽  
Keyword(s):  
Boundary Condition ◽  
Spectral Parameter ◽  
Liouville Problem ◽  
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.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

ON POSITIVE EIGENFUNCTIONS OF STURM-LIOUVILLE PROBLEM WITH NONLOCAL TWO‐POINT BOUNDARY CONDITION

2007 ◽  
Vol 12 (2) ◽  
pp. 215-226 ◽  
Author(s):  
Sigita Pečiulytė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Liouville Problem ◽  
Point Boundary ◽  
Existence Domain ◽  
Classical Boundary ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Nonlocal Boundary Problem

Positive eigenvalues and corresponding eigenfunctions of the linear Sturm‐Liouville problem with one classical boundary condition and another nonlocal two‐point boundary condition are considered in this paper. Four cases of nonlocal two‐point boundary conditions are analysed. We get positive eigenfunctions existence domain for each case of these problems. This domain depends on the parameters of the nonlocal boundary problem and it gives necessary and sufficient conditions for existing positive eigenvalues with positive eigenfunctions.

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