CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

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
Format:   LaTeX   MathJax   PDF  

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 fourth-order linear differential equation, conjugate points, system-conjugate points, subwronskians
MSC Classifications: 47E05, 34B05, 34C10 show english descriptions Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)
Linear boundary value problems
Oscillation theory, zeros, disconjugacy and comparison theory
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
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/