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Comparison Theorem for Conjugate Points of a Fourth-order Linear Differential Equation |
Canad. Math. Bull. 56(2013), 39-43
Published:2011-09-19
Printed: Mar 2013
Printed: Mar 2013
- Jamel Ben Amara,
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 |