Basis properties of root functions of a regular fourth order boundary value problem

Abstract

In this paper, we consider the following boundary value problem y ((4)) + q (x) y = lambda y, 0 < x < 1, y''' (1) - (-1)(sigma) y''' (0) + alpha y(0) = 0, y((s)) (1) - (-1)(sigma) y ((s)) (0) = 0, s = (0, 2) over bar, where lambda is a spectral parameter,