Oscillation criteria of a class of fourth order differential equations

In the present paper, we consider the oscillation of a class of self‐adjoint fourth order differential equation. Some oscillation and non‐oscillation criteria on a perturbation equation of Euler differential equation are given. In particular, we find the exact value of a constant in some oscillation criteria, which has answered the open problem presented by Do?lý in 2004. Copyright © 2011 John Wiley & Sons, Ltd.     

Relative oscillation of linear Hamiltonian differential systems

We discuss the concept of relative oscillation for linear Hamiltonian differential systems. We prove a statement which enables to study this oscillation using the criteria of the classical oscillation theory. We also discuss some other aspects of the problem.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

一类二阶非线性变时滞微分方程的振动准则

研究二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0,对振动因子p(t)变符号的情况讨论了方程的振动性,通过两个已有引理得到了方程振动的两个充分条件.所得结论推广了原有的二阶非线性微分方程与变时滞微分方程当系数不变号时的振动性结论,完善了具变符号振动因子的二阶非线性变时滞微分方程的研究.     

Oscillation behavior of solution of impulsive fractional differential equation

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.     

一类脉冲中立型抛物系统振动性

考虑一类具高阶Laplace算子的脉冲中立型抛物偏微分系统的振动性,借助于一阶脉冲时滞微分不等式,得到了该类系统在Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

脉冲时滞抛物型偏微分方程组解的振动性

研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

脉冲中立型时滞抛物偏微分方程组的振动准则

考虑一类脉冲中立型时滞抛物偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在Robin,Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

具多偏差变元的一阶泛函微分方程的振动性

本文首先考虑多时滞泛函微分方程的振动性,给出了方程振动的几个新的充分条件.然后,把这些结果推广到微分不等式,并应用于多时滞中立型方程的振动性.     

On oscillation of nonlinear second-order differential equations with damping term

The paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term. First it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question, and vice versa. Advantages and drawbacks of such translation are carefully examined. Then an oscillation criterion for the new class of equations is established. The principal result of the paper is compared to those reported in the literature, and an illustrative example to which known oscillation criteria fail to apply is provided.     

非线性中立抛物型偏微分方程系统的振动性定理

研究一类非线性中立抛物型时滞偏微分方程系统解的振动性质,利用积分不等式和泛函微分方程的某些结果,获得了该类系统在第一类边值条件下所有解振动的若干充分条件.结论充分表明振动是由时滞量引起的.     

具脉冲和时滞影响的非线性抛物系统边值问题的振动结果

研究一类具非线性扩散项的脉冲时滞抛物偏微分系统解的振动性,借助Green公式、垂直相加法和脉冲时滞微分不等式,获得了该类系统在Robin边值条件下振动的充分性条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

Delayed feedback control of a chemical chaotic model

The Willamowski–Rössler model system is investigated. It has been found that the system can be locked in a special district: stable without oscillation, periodic-1 oscillation, periodic-2 oscillation by the time delayed feedback. Numerical simulation result has also shown that the initial condition can affect the result of chaos controlling.     

Oscillation and stability of nonlinear neutral impulsive delay differential equations

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

Non-linear oscillation of the fluid in a plate capacitor

Employing the principle of virtual work the equation of motion for the liquid between two electrode walls of a charged parallel plate capacitor is established. Analysis in phase plane stands out the motion is non-linear oscillation. The phase orbit is determined then the oscillation period is expressed with elliptic integrations. Besides the intrinsic parameters in the system, the initial disturbing conditions affect the oscillation period, which readily demonstrates the non-linearity of oscillation. The characters of the period are discussed and the approximate computation is presented. Further, the threshold of control voltage under which the results can be still used for the capacitor with an inclined plate is achieved.     

Oscillation and other properties of linear impulsive and nonimpulsive delay equations

Many of the oscillation results for linear impulsive equations were justified by the following scheme. First, the equivalence of the oscillation of the impulsive equation and some specially constructed nonimpulsive equation was established; further, on the base of well-known results for the nonimpulsive case, the oscillation of the impulsive equation was analyzed. In the present paper, we prove the “oscillation equivalence” result for a linear impulsive equation with a distributed delay and discuss the possibility to expand this approach to the other properties of impulsive equations, for example, stability and asymptotic behavior. In addition, a linear impulsive equation of the second order is considered.     

一类具变号系数的二阶非线性变时滞微分方程的振动性

研究一类二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0的振动性,对振动因子p(t)可变符号的情况,通过两个引理,得出了方程振动的两个充分性定理.所得结论推广了二阶非线性变时滞微分方程当系数不变号时的振动性结论.     

Oscillatory properties of certain nonlinear fractional nabla difference equations

In this paper, we investigate the oscillation of a class of nonlinear fractional nabla difference equations. Some oscillation criteria are established.     

Oscillation criteria for boundary value problems of high-order partial functional differential equations

In this paper, a class of boundary value problems associated with high-order partial functional differential equations with distributed deviating arguments is investigated. Some oscillation criteria of solutions to the problem are developed. Our approach is to reduce the multi-dimensional oscillation problem to a one-dimensional oscillation one by employing some integral means of solutions and introducing some parameter functions. One illustrative example is considered.