Minimality Conditions for Sturm-Liouville Problems with a Boundary Condition Depending Affinely or Quadratically on an Eigenparameter
Date Issued
2024
Author(s)
Kerimov, Nazim
Aliyev, Yagub
Abstract
In the paper we study Sturm-Liouville problems with a boundary condition depending affinely or quadratically on an eigenparameter. The
necessary and sufficient conditions for minimality and completeness of the chosen system of root functions of the corresponding operator were given in two
forms, one with the use of special associated functions and another one with
the direct use of characteristic functions. This direct method was known for
the affine case and was extensively discussed in the literature. The aim of the
present paper is to develop this direct method for the quadratic case and to
consider the affine and quadratic cases together in a unified way
necessary and sufficient conditions for minimality and completeness of the chosen system of root functions of the corresponding operator were given in two
forms, one with the use of special associated functions and another one with
the direct use of characteristic functions. This direct method was known for
the affine case and was extensively discussed in the literature. The aim of the
present paper is to develop this direct method for the quadratic case and to
consider the affine and quadratic cases together in a unified way