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

Abstract

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),whereq(t)ande(t)are continuous functions on[t0,∞),1>λ>0andτ≠0are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the caseτ>0and the caseτ<0under the assumption that the potentialsq(t)ande(t)change signs on[t0,∞).