scholarly journals STURM-LIOUVILLE PROBLEM FOR STATIONARY DIFFERENTIAL OPERATOR WITH NONLOCAL INTEGRAL BOUNDARY CONDITION

2005 ◽  
Vol 10 (4) ◽  
pp. 377-392 ◽  
Author(s):  
S. Pečiulyte ◽  
O. Štikoniene
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Liouville Problem ◽  
Complex Case ◽  
Integral Boundary ◽  
Sturm Liouville ◽  
Nonlocal Integral Boundary Conditions

The Sturm‐Liouville problem with various types of nonlocal integral boundary conditions is considered in this paper. In the first part of paper we investigate Sturm‐Liouville problem with two cases of nonlocal integral boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such problem in the complex case. In the second part we investigate real eigenvalues case. The spectrum depends of these problems on boundary condition parameters is analyzed. Qualitative behaviour of all eigenvalues subject to nonlocal boundary condition parameters is described. Šiame straipsnyje nagrinejamas Šturmo‐Liuvilio uždavinys su viena nelokaliaja integralinio tipo kraštine salyga. Pirmoje straipsnio dalyje tiriamas Šturmo‐Liuvilio uždavinys su dvieju tipu integraline nelokaliaja salyga. Irodytos tikriniu funkciju ir tikriniu reikšmiu bendrosios savybes komplesineje plokštumoje. Antroje dalyje plačiau ištirtas realiuju tikriniu reikšmiu atvejis. Straipsnyje nagrinejama kaip Šturmo‐Liuvilio uždavinio spektras priklauso nuo kraštiniu salygu parametru. Priklausomai nuo nelokaliuju kraštiniu salygu parametru, aprašytas kokybinis tikriniu reikšmiu pasiskirstymas.

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.

scholarly journals Investigation of the spectrum for the Sturm–Liouville problem with one integral boundary condition

2010 ◽  
Vol 15 (4) ◽  
pp. 501-512 ◽  
Author(s):  
A. Skučaitė ◽  
K. Skučaitė-Bingelė ◽  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Liouville Problem ◽  
Characteristic Functions ◽  
Integral Boundary ◽  
Sturm Liouville ◽  
Nonlocal Integral Boundary Conditions ◽  
Type Boundary ◽  
Type Boundary Condition

In this paper, the Sturm–Liouville problem with one classical first type boundary condition and other nonlocal integral boundary conditions of two cases is investigated. We analyze how complex eigenvalues of these problems depend on the parameters of nonlocal integral boundary conditions. Some new results are given on complex spectra of these problems. Many results are presented as graphs of complex characteristic functions.

scholarly journals Relations between Spectrum Curves of Discrete Sturm-Liouville Problem with Nonlocal Boundary Conditions and Graph Theory. II

2021 ◽  
Vol 62 ◽  
pp. 1-8
Author(s):  
Jonas Vitkauskas ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Graph Theory ◽  
Boundary Conditions ◽  
Critical Points ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Sturm Liouville

In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary 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 Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
Kristina Bingelė ◽  
Agnė Bankauskienė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Function Method ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Integral Condition ◽  
Trapezoidal Rule ◽  
Integral Type ◽  
Integral Boundary ◽  
Sturm Liouville

This paper presents new results on the spectrum on complex plane for discrete Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters: γ, ξ1 and ξ2. The integral condition is approximated by the trapezoidal rule. The dependence on parameter γ is investigated by using characteristic function method and analysing spectrum curves which gives qualitative view of the spectrum for fixed ξ1 = m1 / n and ξ2 = m2 / n, where n is discretisation parameter. Some properties of the spectrum curves are formulated and illustrated in figures for various ξ1 and ξ2. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

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.

scholarly journals Distribution of the critical and other points in boundary problems with nonlocal boundary condition

2007 ◽  
Vol 47 ◽  
pp. 405-410
Author(s):  
Sigita Pečiulytė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Characteristic Function ◽  
Critical Points ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Integral Boundary Condition ◽  
Boundary Problems ◽  
Integral Boundary ◽  
Sturm Liouville

In this paper the Sturm–Liouville problem with one classical and other nonlocal two-point or integral boundary condition is investigated. There are critical points of the characteristic function analysed. We investigate how distribution of the critical points depends on nonlocal boundary condition parameters.

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