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

Published:2011-09-19
Printed: Mar 2013
• Jamel Ben Amara,
Faculté des Sciences de Bizerte, Tunisia
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## 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 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.
 Keywords: fourth-order linear differential equation, conjugate points, system-conjugate points, subwronskians
 MSC Classifications: 47E05 - Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) 34B05 - Linear boundary value problems 34C10 - Oscillation theory, zeros, disconjugacy and comparison theory

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