BVP's with discontinuities at finite number interior points and spectral parameter in the boundary conditions

TL;DR

This paper investigates a class of boundary value problems with discontinuities at interior points and spectral parameters in boundary conditions, deriving asymptotic formulas for eigenvalues and eigenfunctions.

Contribution

It introduces new approaches to analyze BVPs with interior discontinuities and eigen-dependent boundary conditions, extending classical Sturm-Liouville methods.

Findings

Asymptotic formulas for eigenvalues derived

Eigenfunctions' behavior characterized at discontinuities

Methodology extends classical Sturm-Liouville theory

Abstract

In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we find asymptotic formulas for the eigenvalues and eigenfunction.