On Eventually Positive Solutions of Quasilinear Second-Order Neutral Differential Equations

Existence for Eventually Positive Solutions of High-Order Nonlinear Neutral Differential Equations with Distributed Delay

Oscillation of Solutions of Second Order Neutral Differential Equations with Positive and Negative Coefficients

In this paper we obtain oscillation criteria for solutions of homogeneous and nonhomogeneous cases of second order neutral differential equations with positive and negative coefficients. Our results improve and extend the results of Manojlović, Shoukaku, Tanigawa and Yoshida [6].

Throughout Positive Solutions of Second-order Nonlinear Differential Equations

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

Positive Periodic Solutions for Second-order Differential Equations with Generalized Neutral Operator

By some analysis of the neutral operator (Ax)(t) = x(t)− ∑n i=1 cix(t− δi) and an application of the fixed-point index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a second-order differential equation with the prescribed neutral operator, which improve and extend some recent results of Lu-Ge, WuWang, and Zhang. An example is ...

Oscillation Results for Even-order Quasilinear Neutral Functional Differential Equations

In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to evenorder quasilinear neutral differential equation “ˆ` x(t) + p(t)x(τ(t)) ́(n−1) ̃γ”′ + q(t)x ` σ(t) ́ = 0, t ≥ t0. Our main results are illustrated with examples.