Asymptotic expressions of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary conditon

TL;DR

This paper derives asymptotic formulas for eigenvalues and eigenfunctions of a discontinuous boundary-value problem with retarded argument, relevant to various scientific fields involving differential equations with delays.

Contribution

It provides new asymptotic expressions for eigenvalues and eigenfunctions of a specific class of differential equations with retarded arguments and boundary conditions involving spectral parameters.

Findings

Asymptotic formulas for eigenvalues derived

Asymptotic expressions for eigenfunctions obtained

Applicable to systems in physics, economics, and biophysics

Abstract

The aim of this study is to find asymptotic expressions of eigenvalues and eigenfunctions of a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition. Applications of differential equations with retarded argument can be encountered in the theory of selfoscillatory systems, in the study of problems connected with combustion in rocket engines, in a number of problems in economics, biophysics, and many other fields. The problems in these areas can be solved reducing differential equations with retarded argument. In this study discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition were investigated and asymptotic formulas were obtained for eigenvalues and eigenfunctions for using areas which mentioned above