Displaying similar documents to “Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions.”

Discrete spectrum and principal functions of non-selfadjoint differential operator

Gülen Başcanbaz Tunca, Elgiz Bairamov (1999)

Czechoslovak Mathematical Journal

Similarity:

In this article, we consider the operator L defined by the differential expression ( y ) = - y ' ' + q ( x ) y , - < x < in L 2 ( - , ) , where q is a complex valued function. Discussing the spectrum, we prove that L has a finite number of eigenvalues and spectral singularities, if the condition sup - < x < exp ϵ | x | | q ( x ) | < , ϵ > 0 holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.

A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem

Jamel Ben Amara (2011)

Colloquium Mathematicae

Similarity:

We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string. ...

Spectral Theory of Singular Hahn Difference Equation of the Sturm-Liouville Type

Bilender P. Allahverdiev, Hüseyin Tuna (2020)

Communications in Mathematics

Similarity:

In this work, we consider the singular Hahn difference equation of the Sturm-Liouville type. We prove the existence of the spectral function for this equation. We establish Parseval equality and an expansion formula for this equation on a semi-unbounded interval.