A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

In this paper, by means of monotone iterative technique, a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established, the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given. In the end, two classes extending boundary value differential systems are discussed and some further results are obtained.     

A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions

In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions

     

Boundedness of solutions for second order differential equations with asymmetric nonlinearity

In this paper we are concerned with the boundedness of all solutions of the second order differential equations

     

非线性抛物型时滞微分方程解振动的充要条件

讨论了一类多滞量非线性抛物型时滞微分方程解的振动性质，获得了其一切解振动的充要条件；指出了其与普通抛物型偏微分方程解的质的差异。     

一类二阶非线性微分系统有界性与收敛性的充分必要条件

本文给出了如下一类二阶非线性微分系统 解的有界性的一些新的充分条件,获得了（Ｓ’）的所有解有界或收敛到零的充分必要 条件．所获的结果能够应用于Ｌｉｅｎａｒｄ类型方程 它改进与扩展了［１,２］等文献关于同样问题的一些重要结果．     

Boundedness of solutions for a class of oscillating potentials without the twist condition

In this paper, we prove that the second order differential equation d^2x/dt^2＋x^2n_1f（x）＋p（t）=0with p（t ＋ 1） = p（t）, f（x ＋ T） = f（x） smooth and f（x） 〉 0, possesses Lagrangian stability despite of the fact that the monotone twist condition is violated.     

具无限时滞中立型泛函微分方程解的稳定性与有界性

以相空间为基础，研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性，建立了方程解为一致稳定，一致渐近稳定的充要性判据；证明了当方程右端泛函满足Lipschitz条件时，解的一致渐近稳定性蕴涵了有界解的存在性，推广了文献［4-6］中已有的相关结果.     

Two unsolved problems in the stability theory of stochastic differential equations with delay

Two unsolved problems of the stability theory for stochastic differential equations with delay are offered for consideration.     

Boundedness of solutions of second order nonlinear dynamic equations

This paper deals with the boundedness of the solutions of the following dynamic equations(r(t)x△(t))△+a(t)f(xσ(t))+b(t)g(xσ(t))=0and(r(t)x△(t))△+a(t)xσ(t)+b(t)f(x(t-τ(t)))=e(t)on a time scale T.By using the Bellman integral inequality,we establish some suffcient conditions for boundedness of solutions of the above equations.Our results not only unify the boundedness results for differential and difference equations but are also new for the q-difference equations.     

Boundedness of solutions for semilinear reversible systems

In this paper we will study the boundedness of all solutions for second-order differential equations

where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.

     

非线性微分方程的正周期解

§ 1　 IntroductionIn[1 ] ,Saker and Agarwal studied the existence and uniqueness of positive periodicsolutions of the nonlinear differential equationN′(t) =-δ(t) N(t) + p(t) N(t) e- a N(t) ,(1 )whereδ(t) and p(t) are positive T-periodic functions.They proved that if p* >δ* ,then(1 ) has a unique T-periodic positive solution,wherep* =min0≤ t≤ Tp(t) ,δ* =max0≤ t≤ Tδ(t) .　　In view ofthe papermentioned above,whatcan be said aboutequation(1 ) when p* ≤δ* ?In this paper,we conside…     

Boundedness of solutions for asymmetric Duffing equations

In this paper, we are concerned with the boundedness of all the solutions and the existence of quasiperiodic solutions for some Duffing equations , where e(t) is of period 1, and g : R → R possesses the characters: g(x) is superlinear when x ? d₀, d₀ is a positive constant and g(x) is semilinear when x ? 0.     

On solutions of third order nonlinear differential equations

The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.     

n阶非线性常微分方程非线性k点边值问题解的存在性

利用格林函数和上下解方法讨论了n阶非线性常微分方程之几类具有非线性k点边界条件的边值问题的存在性。     

一类广义凸函数的充要条件

本文给出了广义梯度的广义单调性定义,借助这些定义给出了一类广义凸函数的充要条件。     

Boundedness of solutions for impulsive differential equations with integral jump conditions

The boundedness of solutions for certain nonlinear impulsive differential equations are obtained, the jumping conditions at discontinuous points are related to the integral of the past states, rather than a left hand limit at the discontinuous points. These results are obtained by new built impulsive integral inequalities with integral jumping conditions using the method of successive iteration.     

关于广义Liénard系统解振动的充要条件

本文给出了广义Liénard系统解振动的充要条件,所得结果推广和改进了文献[1-6]的主要结果．