OSCILLATION OF FIRST ORDER NONLINEAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH MIXED ARGUMENT

This paper devotes to study the oscillatory behavior of solutions of a first order nonlinear impulsive differential equation with mixed argument. First, without assuming the deviating argument to be retarded or advanced, a sufficient condition is established for all solutions of the differential equation to be oscillatory. Next, a sufficient condition for the differential equation to have nonoscillatoty solution is given. Finally, a sufficient and necessary condition for all solutions of the differential equation to be oscillatory is obtained.     

SCALE-INVARIANT SOLUTION FOR FRACTIONAL ANOMALOUS DIFFUSION EOUATION

Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation. For solving the problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform the scale-invariant solution is obtained in terms of Fox functions. And the series and asymptotic representations for the solution are considered.     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

THE DISTRIBUTION OF ZEROS OF SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A VARIABLE DELAY

In this paper, the distribution of zeros of solutions of the first-order neutral differential equation with a variable delayis studied. The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained.     

Existence of Anti-periodic Solution for Differential Equations

In this paper,we discuss the anti-periodic boundary value problem for a class of first order differential equations.By using homotopy method,we obtain the conditions for the existence of anti-periodic solution for the equation under consideration.This result can be extended to higher order differential equations.     

ON THE STABILITY OF SOLUTIONS TO A CERTAIN FOURTH-ORDER VECTOR DELAY DIFFERENTIAL EQUATION

In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.     

Positive Solutions of Boundary Value Problem for a Coupled System of Nonlinear Third-order Differential Equations

By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.     

PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

We obtain sufficient conditions for the existence of periodic solution to a class of second order neutral functional differential equation,using continuation theorem of the coincidence degree.     

拟线性常微分方程在半无限区间的边值问题

Existence of positive solution is established for boundary value problems of non-singular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.     

Global Weak Entropy Solution of Nonlinear Ideal Reaction Chromatography System and Applications

The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution...     

一类二阶变系数线性微分方程的积分因子解法

通过寻求积分因子f1(x),f2(x),求解一类二阶线性微分方程,包括二阶常系数线性微分方程和二阶Euler方程.     

RBSDE’s with jumps and the related obstacle problems for integral-partial differential equations

The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.     

浅谈黎卡提方程的求解

本文提出了黎卡提方程的种解法，将它转化为二阶齐次线性微分方程，再根据朗斯基定理，得出其通解。     

二阶线性微分方程的解法改进

本改进了二阶线性微分方程的朗期基解法，只要求出转化以后的一阶微分方程或二阶齐次线性微分方程的一个特解，即可求出二阶线性微分方程的通解。     

Oscillation of Second-order Delay Differential Equation

By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and some sufficient condition which ensures that all of the solutions of the aboveequation are oscillatory are obtained.     

Riccati微分方程特解新求法的研究

通过对一般Riccati方程进行初等变换,使之变为特殊的Riccati方程,然后利用公式、观察实验,或利用二阶微分方程的特解,或利用一阶微分方程组的特解等方法,求得这些Riccati方程的特解.     

线性算子双半群及在间断和脉冲微分方程中的应用(英)

研究抽象Ｂａｎａｃｈ空间中线性微微分方程的可解性,利用算子双半群方法,讨论了在确定时间跳跃或脉冲的线性微分方程解的存在性,表明在一定条件下间断或脉冲方程的解存在唯一．     

退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”

In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account.     

完全耦合的正倒向随机微分方程及相应的偏微分方程系统

本文利用完全耦合的正倒向随机微分方程,对一类耦合了一个代数方程的二阶拟线性抛物型偏微分方程系统,给出概率表示。在适当的假设下,得到这类偏微分方程系统粘性解的存在唯一性结果。