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

Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the form where ϕδ (u) = |u |δ –1u; α > 0, β ≥ α, and γ ≥ α are real numbers; k, p, q, e, τ, σ are continuous real-valued functions; τ (t) ≤ t and σ (t) ≥ t with limt ∞τ (t) = ∞. The functions p (t), q (t), and e (t) are allowed to change sign, provided that p (t) and q (t) are nonnegative on a sequence of intervals on which e (t) alternates sign. As an illustrative example we show that every solution of is oscillatory provided that either m1 or m2 or r0 is sufficiently large (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)