Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition
International Journal of Mathematics and Mathematical Sciences, cilt.2004, sa.27, ss.1437-1445, 2004 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2004 Sayı: 27
- Basım Tarihi: 2004
- Doi Numarası: 10.1155/s0161171204203088
- Dergi Adı: International Journal of Mathematics and Mathematical Sciences
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.1437-1445
- Ankara Üniversitesi Adresli: Evet
Özet
We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y″+ (λ-q (x))2y=0, xε□+= [0,∞), subject to the spectral parameter-dependent boundary condition y′ (0)- (aλ+b)y (0)=0 in the space L2 (□+), where a≠±i, b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that Lλ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim X→∞q (X)=0, sup xεR+ {exp (□x) | q′ (x)|}<∞, □>0, hold. Finally we show the properties of the principal functions corresponding to the spectral singularities. Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.