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

Abstract

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 [𝑎(𝑡)[𝑥″(𝑡)]𝛾]′=𝑞(𝑡)𝑓(𝑥[𝜏(𝑡)])+𝑝(𝑡)ℎ(𝑥[𝜎(𝑡)]). Both cases ∫∞𝑎−1/𝛾(𝑠)d𝑠=∞ and ∫∞𝑎−1/𝛾(𝑠)d𝑠<∞ are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.