Oscillatory properties of linear third-order differential equations.

Abstract:

Separation theorems, distribution of zeros of solutions, and disconjugacy criteria for linear third-order differential equations are discussed. For instance, it is proved that the equation $y''’ + py'' + qy’ + ry = 0$, where $p \in C'',q \in C’$, and $r \in C$ on an interval $I$, is disconjugate on $I$ if $p$ does not change sign and if $q \leqq 0,r \geqq 0,q - 2p’ \leqq 0$, and $r - q’ + p'' \leqq 0$ on $I$.