On the oscillation of a class of linear homogeneous third order differential equations (Q2716329)

The authors consider the equation NEWLINE\[NEWLINEy'''+a(t)y''+b(t)y'+c(t)y=0 \tag{\(*\)} NEWLINE\]NEWLINE with \(a(t)\leq 0\), \(b(t)\leq 0\), \(c(t)\leq 0\) and \(b(t)\not \equiv 0\) and \(c(t)\not \equiv 0\) in any neighbourhood of \(+\infty \). It is shown that if equation \((*)\) has at least one oscillatory solution than the set of oscillatory solutions forms a two-dimensional subspace of the solution space (see also \textit{J. M. Dolan} [J. Differ. Equations 7, 367-388 (1970; Zbl 0191.10001)], \textit{W. J. Kim} [Proc. Am. Math. Soc. 26, 286-293 (1970; Zbl 0206.09601)], \textit{F. Neuman} [J. Differ. Equations 15, 589-596 (1974; Zbl 0287.34029)]). They also establish two sufficient conditions for the existence of oscillatory solutions to equation \((*)\).