Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

Boundary Value Problems

Maozhu Zhang¹  Hongxiang Song¹  Kun Li² 

[1] College of Mathematics and Statistics, Taishan University;School of Mathematics Sciences, Qufu Normal University;

关键词: Regular approximation;    Singular Sturm–Liouville problems;    Eigenparameter dependent boundary conditions;   

DOI  :  10.1186/s13661-019-01316-0

来源: DOAJ

【 摘 要 】

Abstract In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

【 授权许可】

Unknown