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

http://dx.doi.org/10.4153/CMB-2011-159-6
Canad. Math. Bull. 56(2013), 39-43

  Published:2011-09-19
 Printed: Mar 2013

In 1961, J. Barrett showed that if the first conjugate point $\eta_1(a)$ exists for the differential equation $(r(x)y'')''= p(x)y,$ where $r(x)\gt 0$ and $p(x)\gt 0$, then so does the first systems-conjugate point $\widehat\eta_1(a)$. 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.