Basis Properties in $${\varvec{L}}_{{\varvec{p}}}$$ L p of Root Functions of Sturm–Liouville Problem with Spectral Parameter-Dependent Boundary Conditions

2017 ◽  
Vol 14 (3) ◽  
Author(s):  
Ziyatkhan S. Aliyev ◽  
Aida A. Dunyamaliyeva ◽  
Yashar T. Mehraliyev
Keyword(s):  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Problem ◽  
Root Functions ◽  
Sturm Liouville ◽  
Parameter Dependent

scholarly journals On Basis Property of Root Functions For a Class Second Order Differential Operator

2020 ◽  
Vol 5 (1) ◽  
pp. 361-368
Author(s):  
Volkan Ala ◽  
Khanlar R. Mamedov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Basis Property ◽  
Second Order ◽  
Order Differential Operator ◽  
Root Functions ◽  
Sturm Liouville

AbstractIn this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions.

scholarly journals Double Discontinuous Inverse Problems for Sturm-Liouville Operator with Parameter-Dependent Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. S. Ozkan ◽  
B. Keskin ◽  
Y. Cakmak
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Weyl Function ◽  
Spectral Sequences ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Parameter Dependent

The purpose of this paper is to solve the inverse spectral problems for Sturm-Liouville operator with boundary conditions depending on spectral parameter and double discontinuities inside the interval. It is proven that the coefficients of the problem can be uniquely determined by either Weyl function or given two different spectral sequences.

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.

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