Asymptotic expansion formulas for eigenvalues and eigenfunctıons of the discontinuous boundary value problem with transmission condition

Abstract

In this paper we investigate the boundary value problem according to a special Hilbert space and define an operator which has the same eigenvalue with the problem defined in this Hilbert space. Therefore the boundary value problem is expressed in the form of operator equation. After than some basic properties of the eigenvalues and eigenfunctions of differential equations are given and asymptotic expansion formulas of eigenvalues and eigenfunctions are obtained.