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

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.

Inverse problem for differential systems having a singularity and turning point of even or odd order

“…Also, in the case when the problem has two turning points inside a finite interval, see [21]. In [28], the authors considered a singular Sturm-Liouville problem with eigenparameter dependent boundary conditions and two singular endpoints. They approximated the spectrum, and the strongly resolvent convergence and norm resolvent convergence of a sequence of the inherited restriction operators were studied.…”

The inverse problem for the heat equation with reflection of the argument and with a complex coefficient

“…In [25,26] the problems with operators containing an involution in lower terms are considered. For results concerning nonclassical spectral problems, we refer the reader to [27][28][29][30].…”