Asymptotic formulas for eigenvalues and eigenfunctions of a new boundary-value-transmission problem

TL;DR

This paper develops asymptotic formulas for eigenvalues and eigenfunctions of a novel boundary-value problem involving eigen-dependent boundary conditions and transmission conditions at an interior point, extending classical Sturm-Liouville methods.

Contribution

It introduces a new class of boundary-value problems with eigen-dependent and transmission conditions, providing asymptotic analysis using modified classical techniques.

Findings

Derived asymptotic formulas for eigenvalues.

Obtained asymptotic expressions for eigenfunctions.

Extended Sturm-Liouville theory to new boundary conditions.

Abstract

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