Spectral properties of Sturm-Liouville operators with local interactions on a discrete set

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Yan, Jun¹  Shi, Guoliang^1,2 

[1] Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China

[2] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

关键词: Sturm-Liouville problems;    Discrete spectrum;    Continuous spectrum;    Distribution potentials;   

DOI  :  10.1016/j.jde.2014.06.017

来源: Elsevier

【 摘 要 】

This paper deals with the spectral properties of the Sturm-Liouville operators generated by the differential expression L(y) = 1/w(-(p(x))y')' + v(x)y) with singular coefficients v(x) in the sense of distributions. In particular, we study the operators with delta-type point interactions at the centers x(k) on the positive half line in terms of energy forms. Necessary and sufficient conditions and also simple sufficient conditions are given for the spectrum of the operators to be discrete. We also prove sufficient conditions on the stability of the continuous spectrum. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free