Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations

Abstract

Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of \[ [y(t) - y(t-\tau )]^{(n)} + Q(t) G(y(t-\sigma )) = 0, \ t \ge 0, \tag $*$ \] where $n \ge 3$ is odd. Sufficient conditions are obtained for all solutions of $(*)$ to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with $(*)$ to oscillate or tend to zero as $t \rightarrow \infty $. In this case, there is no restriction on $n$.