On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator

We study the completeness property and the basis property of the root function system of the Sturm-Liouville operator defined on the segment [0, 1]. All possible types of two-point boundary conditions are considered.

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On the absence of the basis property for the root function system of the Sturm–Liouville operator with degenerate boundary conditions

Doklady Mathematics ◽

10.1134/s1064562416020290 ◽

2016 ◽

Vol 93 (2) ◽

pp. 220-222 ◽

Cited By ~ 1

Author(s):

A. S. Makin

Keyword(s):

Boundary Conditions ◽

Liouville Operator ◽

Root Function ◽

Basis Property ◽

Function System ◽

Sturm Liouville

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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

International Journal of Differential Equations ◽

10.1155/2015/641481 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

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

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2006.11.1.14764 ◽

2006 ◽

Vol 11 (1) ◽

pp. 47-78 ◽

Cited By ~ 4

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.

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