Asymptotic Expressions of Fourth Order Sturm-Liouville Operator with Conjugate Conditions

Abstract

In this paper, it is studied the asymptotic expression of fourth order differential operator with periodic boundary conditions. For this operator, it is also considered conjugate boundary conditions at x=0 which shows discontinuity. For this purpose, firstly asymptotic expression of solutions areobtained. Then by using the the asymptotic formulas of fundamental solutions, asymptotic expression of eigenvalues and eigenfunctions are presented. It is also dealt with the asymptotic expression of same operator with antiperiodic boundary conditions and conjugate conditions