Oscillation of third-order nonlinear functional differential equations with mixed arguments

Abstract

The objective of this paper is to offer sufficient conditions for the oscillation of all solutions and other asymptotic properties of the third-order nonlinear functional differential equation � a(t) � x �� (t) � γ � � = q(t)f (x (τ (t))) + p(t)h (x (σ(t))) with mixed arguments, where both cases � ∞ a −1/γ (s) ds = ∞ and � ∞ a −1/γ (s) ds < ∞ are dealt with. We deduce properties of the studied equations via new com- parison theorems. Our results essentially improve and complement earlier ones. We also repair one interesting result of Grace et al.