Interval oscillation criteria for second order super‐half linear functional differential equations with delay and advanced arguments

Abstract

AbstractSufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the formequation imagewhereϕδ(u) = |u|δ–1u;α> 0,β≥α, andγ≥αare real numbers;k,p,q,e,τ,σare continuous real‐valued functions;τ(t) ≤tandσ(t) ≥twith limt→∞τ(t) = ∞. The functionsp(t),q(t), ande(t) are allowed to change sign, provided thatp(t) andq(t) are nonnegative on a sequence of intervals on whiche(t) alternates sign.As an illustrative example we show that every solution ofequation imageis oscillatory provided that eitherm1orm2orr0is sufficiently large (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)