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

Elgiz Bairamov and M. Seyyit Seyyidoglu

Abstract and Applied Analysis, 2010, vol. 2010, 1-10

Abstract:

Let ð ´ denote the operator generated in ð ¿ 2 ( â„› + ) by the Sturm-Liouville problem: − 𠑦 î…ž î…ž + ð ‘ž ( ð ‘¥ ) 𠑦 = 𠜆 2 𠑦 , ð ‘¥ ∈ â„› + = [ 0 , ∞ ) , ( 𠑦 î…ž / 𠑦 ) ( 0 ) = ( ð ›½ 1 𠜆 + ð ›½ 0 ) / ( ð ›¼ 1 𠜆 + ð ›¼ 0 ) , where ð ‘ž is a complex valued function and ð ›¼ 0 , ð ›¼ 1 , ð ›½ 0 , ð ›½ 1 ∈ ð ’ž , with ð ›¼ 0 ð ›½ 1 − ð ›¼ 1 ð ›½ 0 ≠0 . In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of ð ´ . In particular, we obtain the conditions on ð ‘ž under which the operator ð ´ has a finite number of the eigenvalues and the spectral singularities.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:982749

DOI: 10.1155/2010/982749

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