Asymptotic expressions of eigenvalues and fundamental solutions of a discontinuous fourth-order boundary value problem

TL;DR

This paper derives asymptotic formulas for eigenvalues and fundamental solutions of a complex fourth-order boundary value problem with discontinuities and eigenparameter-dependent conditions, aiding advanced spectral analysis.

Contribution

It introduces new asymptotic expressions for eigenvalues and solutions of a discontinuous fourth-order boundary value problem with transmission conditions.

Findings

Asymptotic formulas for eigenvalues derived

Fundamental solutions characterized asymptotically

Applications for boundary value problem analysis

Abstract

In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. Following Mukhtarov and his students methods [2,4,6] we obtain asymptotic formulae for its eigenvalues and fundamental solutions. Our applications possess a number of interesting properties for studying in boundary value problems which we state in this paper.