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 formwhere ϕ δ ( u ) = | u | δ –1 u ; 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 lim t →∞ 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 ofis oscillatory provided that either m 1 or m 2 or r 0 is sufficiently large (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)