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Property (B) and oscillation of third-order differential equations with mixed arguments

Dzurina J, Baculikova B

Journal of Applied Analysis

2013

Vol. 19, nr 1

55--68

In the paper we present sufficient conditions for property (B) and the oscillation of the third-order nonlinear functional differential equation with mixed arguments [α(t)[x(t)] γ]’=q(t)f(x[τ(t)])+p(t)h(x[σ(t)]), where ∫∞α-1/γ(s)ds=∞. We deduce properties of the studied equations by establishing new comparison theorems so that property (B) and the oscillation are resulted from the oscillation of suitable first order equations.