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

✍ Scribed by A. Zafer

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 122 KB
• Volume: 282
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610801

✦ Synopsis

Abstract

Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the form
equation image
where 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 of
equation image
is oscillatory provided that either m~1~ or m~2~ or r~0~ is sufficiently large (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)