Abstract and Applied Analysis
Volume 2011 (2011), Article ID 358912, 12 pages
http://dx.doi.org/10.1155/2011/358912
Research Article

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

Nihal Yokuş

Department of Mathematics, Karamanoğlu Mehmetbey University, 70100 Karaman, Turkey

Received 8 March 2011; Accepted 5 April 2011

Academic Editor: Narcisa C. Apreutesei

Copyright © 2011 Nihal Yokuş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the operator 𝐿 generated in 𝐿 2 ( ℝ + ) by the differential expression 𝑙 ( 𝑦 ) = − 𝑦 + 𝑞 ( 𝑥 ) 𝑦 , 𝑥 ∈ ℝ + ∶ = [ 0 , ∞ ) and the boundary condition 𝑦 ( 0 ) / 𝑦 ( 0 ) = 𝛼 0 + 𝛼 1 𝜆 + 𝛼 2 𝜆 2 , where 𝑞 is a complex-valued function and 𝛼 𝑖 ∈ ℂ , 𝑖 = 0 , 1 , 2 with 𝛼 2 ≠ 0 . In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of 𝐿 .