On Spectral Periodicity for the Sturm–Liouville Problem: Cantor Type Weight, Neumann and Third Type Boundary Conditions

2013 ◽  
pp. 509-516 ◽  
Author(s):  
A. A. Vladimirov ◽  
I. A. Sheipak
Keyword(s):  
Boundary Conditions ◽  
Liouville Problem ◽  
Sturm Liouville ◽  
Type Boundary

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.

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 On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

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