A note on the oscillation of third-order delay differential equations

Abstract

In the paper, we complement existing oscillation criteria for linear third-order delay differential equations by establishing novel sufficient conditions for the nonexistence of so-called Kneser solutions (nonoscillatory solutions with alternating signs of their derivatives). The significant extent of our improvement over known results is illustrated by the example provided. Furthermore, the technique developed here is novel and admits a broad range of possible generalizations, as is discussed in the concluding part of the paper.