Abstract and Applied Analysis

Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter

Elgiz Bairamov and M. Seyyit Seyyidoglu

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Abstract

Let A denote the operator generated in L 2 ( R + ) by the Sturm-Liouville problem: - y ′′ + q ( x ) y = λ 2 y , x R + = [ 0 , ) , ( y / y ) ( 0 ) = ( β 1 λ + β 0 ) / ( α 1 λ + α 0 ) , where q is a complex valued function and α 0 , α 1 , β 0 , β 1 C , with α 0 β 1 - α 1 β 0 0 . In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of A . In particular, we obtain the conditions on q under which the operator A has a finite number of the eigenvalues and the spectral singularities.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 982749, 10 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620702

Digital Object Identifier
doi:10.1155/2010/982749

Mathematical Reviews number (MathSciNet)
MR2601223

Zentralblatt MATH identifier
1198.47062

Citation

Bairamov, Elgiz; Seyyidoglu, M. Seyyit. Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter. Abstr. Appl. Anal. 2010 (2010), Article ID 982749, 10 pages. doi:10.1155/2010/982749. https://projecteuclid.org/euclid.aaa/1288620702


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