On the Asymptotic Behavior of Noncanonical Third-Order Emden–Fowler Delay Differential Equations with a Superlinear Neutral Term

The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay

Oscillatory and Asymptotic Behavior of Third-order Neutral Differential Equations with Distributed Deviating Arguments

This article concerns the oscillatory and asymptotic properties of solutions of a class of third-order neutral differential equations with distributed deviating arguments. We give sufficient conditions for every solution to be either oscillatory or to converges to zero. The results obtained can easily be extended to more general neutral differential equations and neutral dynamic equations on ti...

Oscillation of Third-Order Neutral Delay Differential Equations

and Applied Analysis 3 Theorem 2.1. Assume that 1.4 holds, 0 ≤ p t ≤ p1 < 1. If for some function ρ ∈ C1 t0,∞ , 0,∞ , for all sufficiently large t1 ≥ t0 and for t3 > t2 > t1, one has lim sup t→∞ ∫ t t3 ⎛ ⎜⎝ρ s q s (1 − p τ s ) ∫τ s t2 (∫v t1 1/a u du/b v ) dv ∫s t1 1/a u du − a s ( ρ′ s )2 4ρ s ⎞ ⎟⎠ds ∞, 2.1 ∫∞

Oscillatory and Asymptotic Behavior of Solutions of Second Order Neutral Delay Differential Equations with “maxima”

The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...