The spectrum of eigenparameter-dependent discrete Sturm-Liouville equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

Bairamov, Elgiz¹  Aygar, Yelda¹  Koprubasi, Turhan¹ 

[1] Ankara Univ, Dept Math, TR-06100 Ankara, Turkey

关键词: Discrete equations;    Spectral analysis;    Eigenvalues;    Spectral singularities;   

DOI  :  10.1016/j.cam.2009.12.037

来源: Elsevier

【 摘 要 】

Let us consider the boundary value problem (BVP) for the discrete Sturm-Liouville equation a(n-1)y(n-1) + b(n)y(n) + a(n)y(n+1) = lambda y(n), n is an element of N, (0.1) (gamma(0) + gamma(1)lambda)y(1) + (beta(0) + beta(1)lambda)y(0) = 0, (0.2) where (a(n)) and (b(n)), n is an element of N are complex sequences, gamma(i), beta(i) is an element of C, i = 0, 1, and lambda is a eigenparameter. Discussing the point spectrum, we prove that the BVP (0.1), (0.2) has a finite number of eigenvalues and spectral singularities with a finite multiplicities, if sup(n is an element of N) [exp(epsilon n(delta)) (vertical bar 1 - a(n)vertical bar + vertical bar b(n)vertical bar)] < infinity, for some epsilon > 0 and 1/2 <= delta <= 1. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free