偶数阶中立型偏微分方程系统的振动性定理

讨论了一类偶数阶中立型偏泛函微分方程系统在Robin边界条件下解的振动性,获得了所有解振动的若干充分条件,同时也给出了实际应用例子.     

Linearized oscillations for higher order neutral differential equations

In this paper, the oscillation of certain nonlinear neutral differential equations has been studied with the help of the oscillation of associated linear neutral differential equations     

Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations

The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Linearized oscillation of odd order nonlinear neutral delay differential equations (I)

In this paper, we proved that the odd order nonlinear neutral delay differential equation

[x(t)−p(t)g(x(t−τ))^](n)+q(t)h(x(t−σ))=0     

Comparison theorems for oscillation of second-order half-linear differential equations

Summary We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations. These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous. We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential equation of the general form (|x'|^α-1x')' + a(t) |x|^α-1x = 0.     

Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

Consider the forced higher-order nonlinear neutral functional differential equation

Nonoscillation theorems for second order nonlinear differential equations

We prove nonoscillation theorems for the second order Emden-Fowler equation (E): , , where and . It is shown that when is nondecreasing for any and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when and .

     

Oscillation of second order neutral delay differential equations of Emden-Fowler type

We present new oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)-py(t-τ)]'+ q(t)y ^λ (g(t)) sgn y(g(t)) = 0, t ≧ t ₀. Our results solve an open problem posed by James S.W . Wong [24]. The relevance of our results becomes clear due to a carefully selected example. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类二阶中立型偏泛函微分方程组解的振动性

获得了一类二阶中立型偏泛函微分方程组解振动的若干充分条件．     

一阶中立型时滞微分方程的振动性

分别获得了中立型时滞微分方程「ｘ（ｔ）＋ｐｘ（ｔ－γ」’＋ｑ（ｔ）ｘ（ｔ－σ）＝０的振动性和非振动性的充分条件,其中ｐ〉０,ｑ（ｔ）是一个正的周期函数。     

关于一类偶数阶半线性微分方程解的振动性的注记

通过运用分析方法,对微分不等式进行估计,得到了一类偶数阶半线性微分方程解的振动性的若干判别准则.所得结果减弱了已有文献的条件,推广和改进了已有文献的结果.     

Necessary and sufficient conditions for oscillation of first order nonlinear neutral differential equations

In this paper, we prove that every solution of the first order nonlinear neutral differential equation

     

中立型二阶非线性微分方程振动性的判据

Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms:     

二阶中立型微分方程的振动准则

研究了一类具有连续偏差变元的二阶非线性中立型方程,得到了该类方程的振动准则     

Oscillation criteria for second order nonlinear neutral differential equations

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

(r(t)(x(t)+p(t)x(t-τ))^′)^′+q(t)f(x(t),x(σ(t)))=0.     

Sharp oscillation criteria for second-order neutral delay differential equations

This paper is a continuation of a recent work by the authors on the oscillatory properties of second-order half-linear neutral delay differential equations. Providing a new apriori bound for a nonoscillatory solution, we present a new oscillation criterion, which essentially improves the existing ones. In a particular nonneutral case, the obtained oscillation constant is unimprovable.     

带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则

在本文中,我们获得形如[y(t) l∑j=1pj(t)y(σj(t))](n) ∫0q(t,s)f(y(t s))dσ(s)=h(t)的带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则.     

高阶中立型方程的强迫振动

讨论了一类具有偏差变元的高阶中立型方程，给出了该类方程解振动的充分条件。     

Oscillation of even order nonlinear functional differential equations with damping

This paper is concerned with a class of even order nonlinear damped differential equations