Necessary and Sufficient Conditions for Basis Properties of the System of Root Functions of Sturm-Liouville Boundary Value Problems with Eigenparameter Dependent Boundary Conditions

Abstract

In this study, Sturm-Liouville problems with a boundary condition depending quadratically on an eigenparameter are considered. The necessary and sufficient conditions for minimality and completeness of the chosen system of root functions of the corresponding operator are given in two forms, one of which can be done by direct computations. This computationally simpler way was discussed in the literature for the affine case. But for the quadratic case it was done for a similar boundary value problem only recently. The aim of the present paper is to fill this gap for the quadratic case.