The nonequivalence of oscillation and nondisconjugacy

Abstract

A sufficient condition is given for all solutions of the adjoint of an $n$th order linear differential equation to have an infinity of zeros; an example is presented which shows that for every integer $n > 2$, there exists an $n$th order equation, all of whose solutions have a finite number of zeros, but the adjoint has only solutions with an infinity of zeros. In addition, some open equations on conjugate points are answered.