scholarly journals Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions

2019 ◽  
Vol 68 (2) ◽  
pp. 1316-1334
Author(s):  
Nihal Yokuş ◽  
Esra Kır Arpat
Keyword(s):  
Boundary Conditions ◽  
Spectral Expansion ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

Sturm–Liouville problems with non-separated eigenvalue dependent boundary conditions

2000 ◽  
Vol 130 (2) ◽  
pp. 239-247 ◽  
Author(s):  
P. A. Binding ◽  
P. J. Browne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

Sturm–Liouville differential equations are studied under non-separated boundary conditions whose coefficients are first degree polynomials in the eigenparameter. Situations are examined where there are at most finitely many non-real eigenvalues and also where there are only finitely many real ones.

Darboux transformations and the factorization of generalized Sturm–Liouville problems

2010 ◽  
Vol 140 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Paul A. Binding ◽  
Patrick J. Browne ◽  
Bruce A. Watson
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Darboux Transformation ◽  
Darboux Transformations ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

A version of the Darboux transformation is explored for Sturm-Liouville problems with eigenvalue-dependent boundary conditions, from differential-equation and operator-theoretic viewpoints. Some of the literature on Darboux's transformation is related in a historical introduction.

scholarly journals Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Nihal Yokuş
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Differential Expression ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Complex Valued

We consider the operator generated in by the differential expression , and the boundary condition , where is a complex-valued function and , with . In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of .

scholarly journals Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Elgiz Bairamov ◽  
Nihal Yokus
Keyword(s):  
Boundary Conditions ◽  
Liouville Equation ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Complex Valued

LetLdenote the operator generated inL2(R+)by Sturm-Liouville equation−y′′+q(x)y=λ2y,x∈R+=[0,∞),y′(0)/y(0)=α0+α1λ+α2λ2, whereqis a complex-valued function andαi∈ℂ,i=0,1,2withα2≠0. In this article, we investigate the eigenvalues and the spectral singularities ofLand obtain analogs of Naimark and Pavlov conditions forL.

Spectral properties of Sturm–Liouville system with eigenvalue-dependent boundary conditions

2015 ◽  
Vol 26 (10) ◽  
pp. 1550080 ◽  
Author(s):  
Esra Kir Arpat ◽  
Gökhan Mutlu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Parameter ◽  
Spectral Properties ◽  
Hermitian Matrix ◽  
Boundary Value ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

In this paper, we consider the boundary value problem [Formula: see text][Formula: see text] where λ is the spectral parameter and [Formula: see text] is a Hermitian matrix such that [Formula: see text] and αi ∈ ℂ, i = 0, 1, 2, with α2 ≠ 0. In this paper, we investigate the eigenvalues and spectral singularities of L. In particular, we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities, under the Naimark and Pavlov conditions.

Application of two parameter eigencurves to Sturm–Liouville problems with eigenparameter-dependent boundary conditions

1995 ◽  
Vol 125 (6) ◽  
pp. 1205-1218 ◽  
Author(s):  
P. A. Binding ◽  
Patrick J. Browne
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Theory ◽  
Liouville Problem ◽  
Prüfer Angle ◽  
Sturm Liouville ◽  
Sign Conditions ◽  
Image Position ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Parameter Problem ◽  
Two Parameter

Oscillation, comparison and asymptotic theory for the Sturm-Liouville problemwith 1/p, q, r ε L1 ([0, 1]), p, r > 0, are studied subject to eigenvalue-dependent boundary conditionsThis continues previous work on cases with (− 1)j δj ≦ 0 where δj = ajdj − bjcj. We now consider the remaining sign conditions for δj, exploiting the interplay between the graph of cot θ− (λ, 1), for a modified Prüfer angle θ−, and the eigencurves of a related two-parameter problem.

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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