里卡蒂方法研究带泛函参数的非线性脉冲时滞双曲方程的振动性

本文研究了带泛函参数的非线性脉冲时滞双曲方程的振动性问题.利用积分平均法和里卡蒂方法得到了这类方程解的振动性的一个充分条件,对非线性时滞双曲方程解的震动性进行了推广,能更好地利用一些现有的脉冲时滞常微分方程解的振动性的结论.     

非线性时滞双曲型偏泛函微分方程的振动准则

研究一类多滞量非线性双曲型偏泛函微分方程解的振动性,借助广义Riccati变换和微分不等式技巧,获得了该类方程振动的若干新的充分条件,同时也给出了实际应用的例子.     

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.     

Interval Oscillation Criteria for Nonlinear Neutral Impulsive Differential Equations

In this paper, we study the interval oscillation for nonlinear neutral impulsive differential equations. Sufficient condition for the interval oscillation of the equations is obtained by using Riccati transformation and estimating the ratio of unknown functions $y(t-\sigma(t))$ and $y(t)$. Some known results are generalized and improved. An example is given to illustrate the results.     

具非线性扩散系数的中立双曲型阻尼偏微分方程组解的振动性

研究一类具非线性扩散系数的中立双曲型阻尼偏微分方程组的振动性.通过利用R iccati变换、微积分技巧,获得了该方程组在两类边值条件下解振动的一些充分条件.     

时间测度链上具正负系数的二阶阻尼动力方程的振动准则

研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质.     

Oscillation of second-order nonlinear delay dynamic equations with damping on time scales

By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations with damping on a time scale. Our results extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping.     

OSCILLATION CRITERIA FOR EVEN ORDER DELAY DIFFERENTIAL EQUATIONS WITH NONLINEAR TERM

By Riccati transformation, we establish some new oscillation criteria for a class of even order delay differential equations with nonlinear term. In some sense, the results obtained extend some known results in the literature.     

带强迫项与阻尼项的二阶非线性微分方程的区间振动性

研究了一类二阶非线性微分方程的振动性.利用广义黎卡提变换和积分平均技巧建立了方程(1)的新的振动准则,推广了文献中已有的一些结果.     

Oscillation criteria for certain third-order variable delay functional dynamic equations on time scales

The oscillation of certain third-order nonlinear variable delay functional dynamic equations with nonlinear neutral on time scales is discussed in this article. By using the generalized Riccati transformation and a lot of inequality techniques, some new oscillation criteria for the equations are established. Many of the results are new for the corresponding third-order difference equations and differential equations are as special cases. Some examples are given to illustrate the importance of our results.     

二阶非线性阻尼方程的振动准则

利用Riccati变换和积分平均方法,研究了一类具有阻尼项的二阶非线性方程的解为振动的若干充分条件,建立了一些判定上述方程为振动的充分准则,结果推广并加强了已有的一些振动准则．     

一类二阶非线性泛函微分方程的振动性定理

研究了一类较为广泛的二阶非线性泛函微分方程解的振动性质.在一定条件下,利用广义黎卡提变换、积分平均技巧和分类讨论的方法建立了两个新的振动准则,改进和推广了已知的一些结果.     

一类二阶非线性泛函微分方程的振动性质

研究了一类较为广泛的二阶非线性泛函微分方程解的振动性质.在一定条件下,利用广义黎卡提变换和积分平均技巧建立了方程(1)的两个新的振动准则,推广和改进了已知的一些结果.     

Oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales

In this article, we consider the oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales. Some new sufficient conditions which insure that any solution of the equation oscillates are established by means of an inequality technique and Riccati transformation. This paper improves and generalizes some known results. Several illustrative examples are given throughout.     

一类二阶非线性微分方程的区间振动准则

The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known equations.Finally,several examples illustrate the effectiveness of our results.     

Oscillation and asymptotic behavior of third-order nonlinear neutral delay differential equations with distributed deviating arguments

This paper concerns the oscillation and asymptotic behavior of a class of third-order nonlinear neutral delay differential equations with distributed deviating arguments. By employing a generalized Riccati transformation and integral averaging technique, we establish some sufficient conditions to ensure that all solutions of the considered equations are either oscillatory or converge to zero, which extend and improve some known results in the literature.     

二阶变时滞时标动力系统的振动准则

利用广义Riccati变换及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力系统的振动性,获得了新的振动准则.     

时标上的二阶变时滞动力方程的振动准则

利用广义Riccati技巧及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力方程的振动性,得到了一些新的振动准则.     

Oscillation criteria for a class of neutral difference equations with continuous variable

In this paper, we are mainly concerned with oscillatory behaviour of solutions for a class of second order nonlinear neutral difference equations with continuous variable. Using an integral transformation, the Riccati transformation and iteration, some oscillation criteria are obtained.     

Oscillatory Behavior of Solutions for a Class of Second Order Nonlinear Differential Equation with Perturbation

In this paper, a class of second order nonlinear differential equations with perturbation is studied. By using the generalized Riccati transformation, the integral averaging technique and the method of classification, new oscillation criteria are obtained for all solutions of the equations, which generalize and improve some known results.