On delay-independent criteria for oscillation of higher-order functional differential equations (Q554857)

Summary: We investigate the oscillation of the following higher-order functional differential equation: \[ x^{(n)}(t) + q(t)|x(t - \tau)|^{\lambda - 1}x(t - \tau) = e(t), \] where \(q\) and \(e\) are continuous functions on \([t_0, \infty)\), \(1 > \lambda > 0\) and \(\tau \neq 0\) are constants. Unlike most of the delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case \(\tau > 0\) and the case \(\tau < 0\) under the assumption that the potentials \(q\) and \(e\) change signs on \([t_0, \infty)\).