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

Abstract

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.

Keywords

• Regular approximation
• Singular Sturm–Liouville problems
• Eigenparameter dependent boundary conditions