Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument

Abstract

The purpose of this study is to investigate a Schrodinger type of boundary-value-transmission problem with retarded argument. By modifying some techniques of [S.B. Norkin, Differential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972] and suggesting own approaches, we find asymptotic formulas for the eigenvalues and eigenfunctions of the second-order differential equation with retarded argument, which includes the eigenparameter as a quadratic function.