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

Published online by Cambridge University Press:  20 November 2018

Jamel Ben Amara
Jamel Ben Amara*
Affiliation:
Faculté des Sciences de Bizerte, Tunisia e-mail: jamel.benamara@fsb.rnu.tn
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Abstract

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In 1961, J. Barrett showed that if the first conjugate point ${{\eta }_{1}}\left( a \right)$ exists for the differential equation ${{\left( r\left( x \right){y}'' \right)}^{\prime \prime }}=p\left( x \right)y$, where $r\left( x \right)\,>\,0$ and $p\left( x \right)\,>\,0$, then so does the first systems-conjugate point ${{\hat{\eta }}_{1}}\left( a \right)$. The aim of this note is to extend this result to the general equation with middle term ${{\left( q\left( x \right){y}' \right)}^{\prime }}$ without further restriction on $q\left( x \right)$, other than continuity.

Keywords

47E0534B0534C10fourth-order linear differential equationconjugate pointssystem-conjugate pointssubwronskians
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 39 - 43
Copyright
Copyright © Canadian Mathematical Society 2013

References

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