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

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BAYRAM E., Seyyidoglu M. S.

ABSTRACT AND APPLIED ANALYSIS, cilt.2010, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2010
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/982749
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Ankara Üniversitesi Adresli: Evet

Özet

Let A denote the operator generated in L-2(R+) by the Sturm-Liouville problem: -y(n) + q(x)y = lambda(2)y, x is an element of R+ = [0, infinity), (y'/y)(0) = (beta(1)lambda + beta(0)) = (alpha(1)lambda + alpha(0)), where q is a complex valued function and alpha(0), alpha(1), beta(0), beta(1) is an element of C, with alpha(0)beta(1) - alpha(1)beta(0)not equal 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.