scholarly journals The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions

2021 ◽  
pp. 26-34
Author(s):  
Kadriye AYDEMİR ◽  
Oktay MUKHTAROV
Keyword(s):  
Characteristic Function ◽  
Liouville Problem ◽  
Transmission Conditions ◽  
Sturm Liouville

scholarly journals CHARACTERISTIC FUNCTIONS FOR STURM—LIOUVILLE PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2009 ◽  
Vol 14 (2) ◽  
pp. 229-246 ◽  
Author(s):  
Artūras Štikonas ◽  
Olga Štikonienė
Keyword(s):  
Characteristic Function ◽  
Boundary Conditions ◽  
Function Method ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Characteristic Functions ◽  
Sturm Liouville ◽  
Definition Of

This paper presents some new results on a spectrum in a complex plane for the second order stationary differential equation with one Bitsadze‐Samarskii type nonlocal boundary condition. In this paper, we survey the characteristic function method for investigation of the spectrum of this problem. Some new results on characteristic functions are proved. Many results of this investigation are presented as graphs of characteristic functions. A definition of constant eigenvalues and the characteristic function is introduced for the Sturm‐Liouville problem with general nonlocal boundary conditions.

scholarly journals The Parseval identity for q-Sturm–Liouville problems with transmission conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nida Palamut Koşar
Keyword(s):  
Liouville Problem ◽  
Transmission Conditions ◽  
Spectral Functions ◽  
Expansion Formula ◽  
Sturm Liouville

AbstractIn the present study, we investigate the existence of spectral functions and obtain the Parseval identity and expansion formula in eigenfunctions for the singular q-Sturm–Liouville problem with transmission conditions.

scholarly journals Investigation of Negative Critical Points of the Characteristic Function for Problems with Nonlocal Boundary Conditions

2008 ◽  
Vol 13 (4) ◽  
pp. 467-490 ◽  
Author(s):  
S. Pečiulytė ◽  
O. Štikonienė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Characteristic Function ◽  
Critical Points ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
The Other ◽  
Integral Boundary ◽  
Sturm Liouville

In this paper the Sturm-Liouville problem with one classical and the other nonlocal two-point or integral boundary condition is investigated. Critical points of the characteristic function are analyzed. We investigate how distribution of the critical points depends on nonlocal boundary condition parameters. In the first part of this paper we investigate the case of negative critical points.

scholarly journals Investigation of the spectrum for Sturm–Liouville problems with a nonlocal boundary condition

2013 ◽  
Vol 54 ◽  
pp. 73-78
Author(s):  
Kristina Skučaitė-Bingelė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Characteristic Function ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
The Other ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Type Boundary Condition

In this paper, we analyze the Sturm–Liouville problem with one classical first type boundary condition and the other Samarskii–Bitsadze type nonlocal boundary condition. We investigate how the spectrum of this problem depends on the parameters γ and ξ  of the nonlocal boundary condition. Some new results are given as graphs of the characteristic function.

scholarly journals INVESTIGATION OF SPECTRUM CURVES FOR A STURM-LIOUVILLE PROBLEM WITH TWO-POINT NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
Vol 25 (1) ◽  
pp. 37-52
Author(s):  
Kristina Bingelė ◽  
Agnė Bankauskienė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Characteristic Function ◽  
Boundary Conditions ◽  
Critical Points ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Point Boundary ◽  
Sturm Liouville

The article investigates the Sturm–Liouville problem with one classical and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures for various values of parameter ξ.

scholarly journals SPECTRUM CURVES FOR STURM–LIOUVILLE PROBLEM WITH INTEGRAL BOUNDARY CONDITION

2015 ◽  
Vol 20 (6) ◽  
pp. 802-818 ◽  
Author(s):  
Agnė Skučaitė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Characteristic Function ◽  
Critical Points ◽  
Nonlocal Condition ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Integral Boundary ◽  
Sturm Liouville

We consider Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters γ (multiplier in nonlocal condition), ξ1, ξ2 ([ξ1, ξ2] is a domain of integration). The distribution of zeroes, poles, and constant eigenvalue points of Complex Characteristic Function is presented. We investigate how Spectrum Curves depend on the parameters of nonlocal boundary conditions. In this paper we describe the behaviour of Spectrum Curves and classify critical points of Complex-Real Characteristic function. Phase Trajectories of critical points in Phase Space of the parameters ξ1, ξ2 are investigated. We present the results of modelling and computational analysis and illustrate those results with graphs.

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