Asymptotic Estimations of Eigenvalues and Eigenfunctions for a Multi-point Nonlocal Boundary Value Problem

Abstract

In this paper, the multi-point nonlocal second order linear Sturm-Liouville problem is considered consisting of the equation $ -u^{\prime \prime}(t) + {q}(t) u(t)=\lambda u(t) $ on [0,1] and multi-point boundary value conditions. The geometric multiplicity of eigenvalues, the asymptotic formulas for eigenvalues and eigenfunctions are expressed explicitly under certain mild conditions, these results can be used to investigate the inverse spectral problems of certain Sturm-Liouville operators.