On a Sturm-Liouville Type Problem with Retarded Argument

TL;DR

This paper investigates a Sturm-Liouville problem with retarded argument, spectral parameter in boundary conditions, and transmission conditions at discontinuities, deriving asymptotic formulas for eigenvalues and eigenfunctions.

Contribution

It introduces a Sturm-Liouville problem with retarded argument and boundary conditions involving spectral parameters, providing new asymptotic formulas for eigenvalues and eigenfunctions.

Findings

Derived asymptotic formulas for eigenvalues.

Obtained asymptotic formulas for eigenfunctions.

Analyzed the impact of retarded argument and transmission conditions.

Abstract

In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.