Refinement Asymptotic Formulas of Eigenvalues and Eigenfunctions of a Fourth Order Linear Differential Operator with Transmission Condition and Discontinuous Weight Function

Abstract

In this paper, we promote the refinement method for estimating asymptotic expression of the fundamental solutions of a fourth order linear differential equation with discontinuous weight function and transmission conditions. These refinement solutions utilize more accurate asymptotic formulas for the eigenvalues and eigenfunctions for the problem.

Behavior of the Eigenvalues and Eignfunctions of the Regge-Type Problem

“…Lately, the investigation of the problem of finding eigenvalue has the line of discontinuity on the solutions or coefficients of the differential operator [5][6][7][8][9]. In their article [10], Yang and Wang studied the class of Sturm-Liouville operators with their spectral parameter-dependent boundary conditions and transmission conditions at finite interior points.…”

Comparison Methods for Solving Non-Linear Sturm–Liouville Eigenvalues Problems

“…In [18] they compute eigenvalues and eigenfunctions of singular two-interval Sturm-Liouville problems. While in [19], they solve fourth order linear differential equations. Fractional Sturm-Liouville problem based on the operational matrix method was presented in [20].…”