Abstract view
Comparison Theorem for Conjugate Points of a Fourthorder Linear Differential Equation


Published:20110919
Printed: Mar 2013
Jamel Ben Amara,
FacultÃ© des Sciences de Bizerte, Tunisia
Abstract
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
systemsconjugate 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.