Necessary and Sufficient Conditions for Basis Properties of the System of Root Functions of Sturm-Liouville Boundary Value Problems with Eigenparameter Dependent Boundary Conditions
Date Issued
2024
Author(s)
Aliyev, Yagub
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.
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.