Comparison Theorem for Conjugate Points of a Fourth-order Linear Differential Equation

Abstract

AbstractIn 1961, J. Barrett showed that if the first conjugate point η(a) exists for the differential equation (r(x)y'')'' = p(x)y, where r(x) > 0 and p(x) > 0, then so does the first systems-conjugate point . The aim of this note is to extend this result to the general equation with middle term (q(x)y')' without further restriction on q(x), other than continuity.