Oscillation of Third-Order Differential Equations with Advanced Arguments

Abstract

The main objective of this work was to study some oscillatory and asymptotic properties of a new class of advanced neutral differential equations. Using new relations to link the solution and its corresponding function, we introduced new oscillatory criteria that aim to enhance, simplify, and complement some of current results. We provide some examples to demonstrate the significance of our results.

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

“…On the other hand, we do not need more additional conditions, such as (8). By utilising the results provided in the reference [34], we establish new oscillation criteria for Equation (1). Based on the above, we aim in this paper to complete, simplify, and develop previous results.…”

“…In this work, we establish the new results of the asymptotic and oscillatory behavior of the solutions of the following differential equations with distributed deviating arguments: rg ′ ′ (⊤) + η(⊤)g ′ (⊤) + b a q(⊤, s)κ λ (σ(⊤, s))ds = 0, ⊤ ≥ ⊤ 0 > 0, (1) where λ is quotient of odd positive integers,…”