On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

Abstract EN

We investigate the oscillation of the following higher-order functional differential equation: x(n)(t)+q(t)|x(t-τ)|λ-1x(t-τ)=e(t), where q(t) and e(t) are continuous functions on [t0,∞), 1>λ>0 and τ≠0 are constants.

Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case τ>0 and the case τ<0 under the assumption that the potentials q(t) and e(t) change signs on [t0,∞).