Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments

The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments [()[″()]]′=()([()])+()ℎ([()]). Both cases ∫∞−1/()d=∞ and ∫∞−1/()d<∞ are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

The aim of this paper is to offer a generalization of the Philos and Staikos lemma. As a possible application of the lemma in the oscillation theory, we study the asymptotic properties and oscillation of the nth order delay differential equations (E)(r(t)[x(n−1)(t)]γ)′+q(t)xγ(τ(t))=0. The results obtained utilize also the comparison theorems