带阻尼项的三阶脉冲微分方程的振动性与渐近性

解决了一类带阻尼项的三阶脉冲微分方程的非振动解与其一阶、二阶导数的符号关系,用迭代法得到其振动性与渐近性的判别准则,并举例说明准则的有效性.     

高阶泛函微分方程的振动性和渐近性

本文讨论带有强迫项的时滞型泛函微分方程的振动性和渐近性。对于形如和的方程得到了几个振动及渐近性质的判别准则。本文的结论的证明还修正了R.S.Dahiya在讨论线性方程时出现的错误。     

二阶非线性扰动微分方程的振动性准则

本文主要研究了二阶非线性扰动微方程的振动性,所得的振动性准则包含和推广了一些现有的结果。     

一类带强迫项的二阶脉冲时滞微分方程的振动性

给出引理解决了一类带强迫项的二阶脉冲时滞微分方程的非振动解与其导数的符号关系,得到其振动性与渐近性的判别准则,并举例说明准则的有效性。     

非线性中立型泛函微分方程组的非振动解的存在性准则

本文利用 Banach 锥理论首次建立了非线性中立型泛函微分方程组的非振动解的存在性准则;同时,还给出了非线性高阶中立型方程的振动性和非振动性定理.     

具非正系数的二阶中立型泛函微分方程的渐近性

本文讨论一类具非正系数的二阶中立型泛函微分方程非振动解的渐近性类型与判别,我们给出了非振动解的四种渐近性类型及其判别准则,这些判别准则都是充分必要条件。     

n维非线性中立型时超微分方程组解的振动性

本文首先研究了具有正负号系数的线性中立型时超微分不等式解的振动性。获得了其解振动的判定准则,然后应用该准则研究了非线性中立型时超微分方程和n维非线性中立型时超微分方程组解的振动性。获得其解振动的充分条件。     

二阶非线性微分方程的振动性

本文利用Riccati技巧和平均技巧，研究一类二阶非线性微分方程的振动性，得到了这类方程振动的若干新的判别准则。     

二阶矩阵微分系统的振动性

通过Kummer变换，建立了线性矩阵微分系统(P(t)Y′)′ Q(t)Y=0的振动性判别准则，改进了文[4]，[5]的振动性判别准则，并且简化了文[7]的证明．     

线性矩阵Hamilton系统振动性的区间判据

采用两种不同的方法,得到了线性矩阵Hamilton系统的振动性判据.这些振动性判据仅依赖于系数矩阵在[to,∞)的某些子区间上的性质,从而改进并推广了许多已知的Kamenev型振动准则.     

The numbers of periodic solutions of the polynomial differential equation

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.     

SHARP CRITERIONS OF GLOBAL EXISTENCE AND COLLAPSE FOR COUPLED NONLINEAR SCHRODINGER EQUATIONS

In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schr6dinger equations are derived out in terms of the characteristics of the ground state and the local theories. And the conclusion that how small the initial data are, the global solutions exist is proved.     

On linear stochastic differential games with average cost criterions

In this paper, we consider scalar linear stochastic differential games with average cost criterions. We solve the dynamic programming equations for these games and give the synthesis of saddle-point and Nash equilibrium solutions.The authors wish to thank A. Ichikawa for providing the initial impetus and helpful advice.     

On the Cauchy Problems of Fractional Evolution Equations with Nonlocal Initial Conditions

In this paper, new criterions which allow us to relax the compactness and Lipschitz continuity on nonlocal item, ensuring the existence and uniqueness of mild solutions for the Cauchy problems of fractional evolution equations with nonlocal initial conditions, are established. The results obtained in this paper essentially extend some existing results in this area. Finally, we present two applications to the abstract results.     

二阶NFDE零解的稳定性

本文给出了二阶中立型微分方程ｘ（ｔ）＋ｘ（ｔ－τ）＋ｂｘ（ｔ）＋ｂ１ｘ（ｔ－τ）＋ｃｘ（ｔ）＋ｃ１ｘ（ｔ－τ）＝０零解稳定的代数判据．     

时滞微分方程的稳定性

该文利用时滞Gronwall Bellman不等式得到了一些判定时滞微分方程稳定性的充分条件, 特别地,为方便应用,对线性时滞微分方程给出了一些仅与方程右端项有关的简明判据.     

Attractor Bifurcation and Phase Transition for Liquid <Superscript>4</Superscript>He

Experiments show that the liquid helium-4 has either superfluid phase or solid phase when temperature decreases or the pressure of the system changes. In this paper, we discuss the equations which govern these phase transitions and derive the criterions for these phase changes. Meanwhile, we give related approximate solutions and draw the phase diagram. In addition, we also prove that the liquid helium-4 bifurcates from the trivial solution to an attractor as parameters cross certain critical value. The topological structure of the bifurcated attractor is also illustrated.     

OSCILLATION OF THE SOLUTIONS OF NONLINEAR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.