Search

We present new criteria for asymptotic stability of two classes of nonlinear neutral delay differential equations. By using two auxiliary functions on a contraction condition, we extend the results in [12]. Also we give two examples that illustrate our results.

In this paper we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay. We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show that, under suitable conditions, such maps fit very nicely into the framework of Krasnoselskii-Burton's fixed point theorem so that the existence of periodic solutions is concluded.

In this article we study the existence of positive periodic solutions for a fourth-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other one is completely continuous.

In this article we study the existence of positive periodic solutions of the second-order nonlinear neutral differential equation with variable delay

In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay \[ \frac{d^{2}}{dt^{2}}x\left( t\right) +p\left( t\right) \frac{d}{dt}x\left( t\right) +q\left( t\right) x^{3}\left( t\right) = \frac{d}{dt}g\left( t,x\left( t-\tau\left( t\right) \right) \right) +f\left( t,x^{3}\left( t\right) ,x^{3}\left( t-\tau\left( t\right) \right)\right). \] The main tool employed here is the Burton-Krasnoselskii's hybrid fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.

In this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form $$ \left(r(t)z^{(n-1)}(t)\right)'+q(t)f(x(\sigma(t)))=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)),$ $n\geq2$ is a even integer. The results are obtained both for the case $\int^\infty r^{-1}(t){\rm d}t=\infty,$ and in case $\int^\infty r^{-1}(t){\rm d}t

In this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with infinite distributed delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Han and Ren (Nonlinear Anal, 70:1393-1406, ). [ABSTRACT FROM AUTHOR]

In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x" (t) + p (t) x' (t) + q (t) x³ (t) = c (t) x'(t - τ(t)) + f (t, x³ (t - τ (t))) . The main tool employed here is the Burton-Krasnoselskii's hybrid fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact. [ABSTRACT FROM AUTHOR]

This paper deals with oscillation criteria for even order nonlinear neutral mixed type differential equations of the form ... are ratios of odd positive integers. The results are obtained both for the case ... Some examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Cheung, Ren and Han [7]. [ABSTRACT FROM AUTHOR]

In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay ... x(t) + p(t) ... x(t) + q(t)x³ = ... g(t, x(t - τ (t))) + f(t, x³ (t), x³ (t - τ (t))). The main tool employed here is the Burton-Krasnoselskii's hybrid fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact. [ABSTRACT FROM AUTHOR]

Abstract: By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those in the recent paper by Shi and Wang and related contributions to the subject. Examples are provided to illustrate the relevance of new theorems. [Copyright &y& Elsevier]

Abstract: For a class of -th order nonlinear neutral differential equations, sufficient conditions for all nonoscillatory solutions to satisfy are established. For another class of equations, necessary and sufficient conditions for nonoscillatory solutions to satisfy the above condition are obtained. Our theorems complement and extend recent results reported in the literature. [Copyright &y& Elsevier]

In this paper, we consider the oscillation of a class of third-order nonlinear neutral differential equations with distributed deviating arguments by using comparison principles. The obtained criteria essentially extend and improve related results in the literature by removing some restrictive conditions, which can easily be extended to more general third-order differential equations. Examples are also given to illustrate the established results. [ABSTRACT FROM AUTHOR]