Oscillation theorems for fourth-order quasi-linear delay differential equations

Abstract

<abstract><p>In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $ \mathcal{N}_{a} $. As an extension of the approach taken in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, we establish a new criterion that guarantees that $ \mathcal{N}_{a} = \emptyset $. Then, we create a new oscillation criterion.</p></abstract>

Superlinear distributed deviating arguments to study second-order neutral differential equations

“…Because of this, observation showed a renewed interest in investigating the oscillatory behavior of solutions to (E). As a consequence, the findings that were acquired via the use of this article are novel and add to those found in [9,10,13,23,27,30,31,[33][34][35]37].…”

More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations

“…Let x ∈ Ω 2 , and choose 1 ≥ 0 , such that z(σ( )) > 0 and parts (A 2,1 )-(A 2,3 ) in Lemma 7 hold for ≥ 1 ≥ 0 and choose fixed but arbitrarily large λ ≤ λ * , β ≤ β * , and k ≤ k * satisfying ( 5), (6), and ( 7), respectively, for ≥ 1 . Using (17), and the decreasing of z/π 1/k 12 , we have…”

“…We need to show that they each hold for n + 1. (A n+1,1 ): Using (A n,3 ) in (17), we obtain w ( ) ≥ β z α (σ( ))…”

“…The study of oscillation criteria for higher-order DEs has long captured significant interest within the field, see [15][16][17][18]. Notably, the analysis of third-order NDEs has received attention due to its importance in diverse scientific and engineering fields, from control theory to population dynamics.…”

Analyzing existence, uniqueness, and stability of neutral fractional Volterra-Fredholm integro-differential equations

“…This study might offer valuable perspectives on stability aspects within such models, especially in regimes where attraction dynamics dominate. [4,5,28,29,33,[35][36][37]41] provided remarks on oscillation of second-order neutral differential equations. While not directly related to PDEs, their insights into oscillatory behavior could inform discussions on system dynamics and stability in certain differential equation models.…”