Boundary value problem with transmission conditions
K. Aydemir, O. Sh. Mukhtarov
TL;DR
This paper develops a spectral analysis method using Green's functions for a Sturm-Liouville boundary value problem that includes transmission conditions and eigenparameter-dependent boundary conditions.
Contribution
It introduces a novel approach to analyze Sturm-Liouville problems with transmission conditions using Green's functions in a modified Hilbert space.
Findings
Spectral properties are characterized for the problem.
Green's function method is successfully applied.
The approach handles eigenparameter-dependent boundary conditions.
Abstract
One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function method for spectral analysis of the considered problem in modified Hilbert space.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Advanced Mathematical Modeling in Engineering