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

Amara, Jamel Ben

Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 39-43

Résumé

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.

Détail

DOI : 10.4153/CMB-2011-159-6

Mots-clés : 47E05, 34B05, 34C10, fourth-order linear differential equation, conjugate points, system-conjugate points, subwronskians