一类非自治非线性微分方程周期解的存在性

本文讨论非自治非线性微分方程组■=ф(y)-f(x),■=-g(x)+e(t) (1)周期解的存在性.N.Levinson 曾给出■(y)≡y、g(x)≡x 时系统(1)存在周期解的条件,井竹君推广了文[1]的工作.本文给出方程组(1)存在周期解的一组充分条件,进一步推广了文[2]的结果.     

Banach空间中一类非线性积分微分方程解的存在性

本文利用不动点定理研究Ｂａｎａｃｈ空间中一类非线性积分微分方程解的存在性，推广了一些已知结果。     

一类二阶非线性微分方程组周期解的存在性

本文中,我们把Ragleigh方程推广到n维空间进行讨论,首先给出方程周期解一致界的先验估计,然后利用Mawhin的重合度(Coincidence Degree)理论得到了方程存在周期解的两个充分条件。     

一类二阶微分方程周期解的存在性

研究二阶非线性滞后型微分方程x。(t)+P[x(。t)]+Q[x(。t)]R[x(t-r)]=f(t)通过Lyaponov方法给出了ω-周期解的存在性定理和时滞范围的简明表达式,推广了一些原有结果.     

一类非线性微分方程系统周期解的性

给出了一种基于解的有界性而判定周期解存在性的方法。通过应用比较原理和讨论辅助一维微分方程解的性质得到了本文的主要结果。     

一类非线性微分方程解的存在性

考虑了一类非线性微分方程边值问题.通过应用Krasnoselskii锥不动点定理及不动点指数给出了这类问题解的存在性及多解性.所得结果推广了最近文献中一些相关结论.     

一类三阶非线性常微分方程的周期解

微分方程周期解的存在性问题,很早就受到重视。本文用拓扑度的方法研究一类三阶非线性方程周期的存在性。为方便起见,我们约定本文涉及到的函数都是连续的,对t是ω周期的;并且能保证方程     

凝血动力系统中周期解的存在性

本文对于凝血系统中蛋白C抑制作用的数学模型进行动力学分析，应用Poincare截面及Brouwer不动点定理等工具严格的证明了这一高维动力系统存在周期解。     

一类非线性微分方程极限环的存在性

本文研究了方程: x+f(x)g(x)+φ(x)g(x)=0的极限环存在性问题,推广了文献[9]-[11]的有关结果。     

奇异二阶微分方程积分边值问题正解的存在唯一性

利用上下解方法结合极值原理研究一类带积分边值条件的奇异二阶微分方程正解的存在性以及唯一性,给出了$C[0,1]$和$C^1[0,1]$正解存在唯一的一个充分条件.非线性项允许在$t=0,1$ 和$x=0$处具有奇异性.     

A NOTE ON THE SOLUTION TO NEUMANN BOUNDARY VALUE PROBLEM OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

The author of this paper, by means of the semi-rank theory, establish a new comparative theorem and give the existence of maximal and minimal solutions to Neumann boundary value problems of second order nonlinear differential equation in ordered Banach spaces when the upper and lower solutions in the reversed order of the problem are given.     

EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL DIFFERENTIAL SYSTEM WITH DELAY

This paper is concerned with the existence of solution to nonlinear second order neutral differential equations with infinite delay in a Banach space. Sufficient conditions for the existence of solution are obtained by a Schaefer fixed point theorem.     

EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION TO A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, the existence of almost periodic solution to a second order nonlinear equation is investigated by contraction mapping principle under some conditions. It ought to be noted that using Schauder fixed point theorem to discuss such a problem will cause a failure.     

EXISTENCE OF PERIODIC SOLUTION FOR HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATION

The existence of periodic solutions is proved for the higher order nonlinear differential equation by applying Leray-Schauder principle and Wirtinger's inequality.     

BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

The author studies the boundary value problems for systems of nonlinear second order differential difference equations and adopts a new-type Nagumo condition,in whichthe control function is a vector-valued function of several variables and which can guarantee simultaneoulsy and easily finding a priori bounds of each component of the derivatives of the solutions,Under this new-type Nagumo condition the existence results of solutions are proved by means of differential inequality technique.     

EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.     

Banach空间混合型一阶脉冲积分-微分方程初值问题的唯一解

本文在一般的序Banach空间中研究了一阶脉冲混合型积分-微分方程初值问题的唯一解。在比较广泛的上控制条件并且假定所考虑初值问题只有一个上解或下解的假设之下,我们证明了所考虑初值问题的唯一解可以由显形式表达的迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计,本文没有使用任何紧型条件。我们的结果是最近一些结果的改进和推广。     

EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.