Positiveness of second order differential operators with interior singularity

The main goal of this study is to provide an operator-theoretic framework for the investigation of discontinuous Sturm-Liouville problems with eigenparameter appearing in the boundary conditions. We introduce some self-adjoint compact operators in suitable Sobolev spaces such a way that the consider...

Full description

Saved in:
Bibliographic Details
Main Authors: Mukhtarov, Oktay, Olgar, Hayati, Muhtarov, Fahreddin
Format: Conference Proceeding
Language:English
Subjects:
Boundary conditions
Differential equations
Eigenvectors
Linear operators
Sobolev space
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The main goal of this study is to provide an operator-theoretic framework for the investigation of discontinuous Sturm-Liouville problems with eigenparameter appearing in the boundary conditions. We introduce some self-adjoint compact operators in suitable Sobolev spaces such a way that the considered problem can be reduced to an operator-pencil equation. We define a new concept so-called generalized eigenfunctions and prove positiveness of operator-pencil corresponding to the considered problem.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4959658