Class of Sturm–Liouville Problems with Eigenparameter Dependent Transmission Conditions

ABSTRACT

The objective of this paper is the investigation of a new class Sturm–Liouville problems on two disjoint intervals when the eigenparameter appears not only in the equation but also in the boundary and transmission conditions. We concerned with the problem of justifying some spectral properties of the eigenvalues and corresponding eigenfunctions. Particularly, we examined asymptotic behavior of the eigenvalues and corresponding eigenfunctions.

KEYWORDS:

• Eigenfunction
• eigenparameter-dependent boundary and transmission conditions
• eigenvalue
• Sturm-ŰLiouville problems

MATHEMATICS SUBJECT CLASSIFICATION:

• 34B09
• 34B24