Asymptotic formulas for eigenvalues and eigenfunctions of boundary value problem

TL;DR

This paper develops asymptotic formulas for eigenvalues and eigenfunctions of a new class of boundary value problems with eigendependent boundary conditions and transmission conditions, extending classical Sturm-Liouville methods.

Contribution

Introduces a novel class of boundary value problems with eigendependent and transmission conditions, providing asymptotic formulas using modified Sturm-Liouville techniques.

Findings

Derived asymptotic formulas for eigenvalues

Obtained asymptotic expressions for eigenfunctions

Extended classical Sturm-Liouville methods

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.