Property (A) and Oscillation of Third-Order Differential Equations with Mixed Arguments

Abstract

In this paper we offer criteria for property (A) and the oscillation of the third-order nonlinear functional differential equation with mixed arguments [a(t)[x′(t)]^γ]″ + q(t)f(x[τ(t)]) + p(t)h(x[σ(t)]) = 0, where ∫^∞ a^−1/γ(s)ds = ∞. We deduce properties of the studied equations by establishing new comparison theorems so that property (A) and the oscillation are resulted from the oscillation of a set of the first order equations.