一类微分差分方程的周期解

本文研究微分差分方程ｘ＇（ｔ）＝－ｆ（ｘ（ｔ），ｘ（ｔ－τ１））－ｆ（ｘ（ｔ），ｘ（ｔ－τ２））－．．．－ｆ（ｘ（ｔ），ｘ（ｔ－τｎ））非平凡周期解的存在性问题，得到了一些判别准则，推广和改进了文［１－４］的工作。     

一类微分差分方程的周期解

泛函微分方程周期解的存在性问题是重要而困难的。文[1—3]分别用Kaplan—Yorke方法研究了含一个滞量的微分差分方程的周期解问题。文[4]用Kaplan-Yorke方法研究了含二个滞量的微分差分方程周期解的存在性问题。本文研究微分差分方程     

某些微分差分方程的周期解

本文给出了微分差分方程及 x′(t)=-g(x(t))F(x(t),x(t-1))x′(t)=-g(x(t))F(x(t),x(t-1),…,x(t-n))存在非平凡周期解的充分条件。     

关于微分差分方程组周期解的存在性

目前,对泛函微分方程周期解的存在性问题的研究,主要用不动点原理这个工具,这种方法可用丁证明周期解的存在,但较少涉及周期解的个数与周期。本文采用了一种构造性方法去研究微分差分方程组周期解的存在性,这种方法是由Kaplan与Yorke所引入,井被温立志改进了的,原来被用于研究标量方程,在本文中,首次将它用于研究方程组,     

一类二阶中立型微分差分方程周期解的存在性

考虑如下二阶中立型微分差分方程的边值问题：{x(t-τ)-x(t-τ） f(t,x(t),x(t-τ）,x(t-2τ）=0 x(0)=x(2kτ），x（0）=x（2kτ）其中k是任意给定的正整数,τ 为正实数，利用含有偏差变元的变分结构及临界点理论，作给出了判定上述方程存在非平凡周期解的判定准则。     

一类三维微分差分方程组非平凡周期解的存在性

本文研究了一类三维自治微分差分方程组非平凡周期解的存在性问题并得到了新的结果.本文方法不但适用于滞后系统,而且适用于同时具有超前变元的混合型系统.     

一类混合型微分差分方程的周期解

利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件.     

一类非线性微分差分方程的近似解

本文对一类非线性微分差分方程求得一致有效渐近展开式,给出了共振解的近似解析表达式,并推广了Nayfeh和Mook的结果.     

关于一类微分方程周期解定理的推广

本研究了一种微分差分方程周期解的存在性,并且获得了它们具有非平凡周期解的充分条件,推广了[1]-[5]的工作。     

几类三阶非线性微分差分方程平凡解的稳定性

本文讨论几类三阶非线性微分差分方程平凡解的稳定性,为了作出恰当的泛函,我们使用J.A.Walker、L.G.Clark的积分法并加以改进。从而得到若干充分性条件。这些条件简单,易于实现。     

高阶微分方程允许解的存在性

本文主要目的是利用值分布理论研究复高阶微分方程(Ω(z,w)/w^k0(w’)^k1…(w^(n)^kn)^m=aw^p ∑j=0^s bj(z)w^j,(p≥m）亚纯允许解的存在性问题．证明了一个在适当的条件下，该微分方程的亚纯解一定不是允许解的结果．实例表明该文的结果是最佳的．     

ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

51.IntroductionDtherelltial-iterativeequationisakindofspecialfunctionaldmerelitialequationswhichwerediscussedrecently[1--6].Mostoftheresearche.[1--3]nowavailablefocusedontheeln-tenceofautonomousdifferential-iterativeequationintheformofwherex(2)=x(x(t))andx(k)=x(x(*--')(t)),k=3,4,'In,andsomeintheml4--5]dealtwiththeequatiollx'(t)~(a'--xZ(t))f(x(")(t)).Weproposedatransformationtheoremin[6]andusedittodiscusstheetistenceandbehaviorofsolutionstotheequationx'(t)'=.ax(t)--b-c(x(t)),where0相似文献   

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

THE EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper, a fixed point theorem in C1[0,1] space is established using the properties of the fixed point index. This theorem is applied to prove the existence of positive solution to the boundary value problems of second order differential equations.     

中立型方程正解的存在性

一、引言近年来有大量文章研究中立型泛函微分方程的解的振动性质,但对正解的存在性结果相对说是不多的.最近 Jaros 和 Kusano 系统地研究了高阶中立型微分方程的非振动解的存在性.他们证明中立型微分方程     

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.     

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH RESPECT TO SEMIMARTINGALES

Papers [1, 2] deal with the problem of the existence and uniqueness of the solutions of two different stochastic differential equations with respect to semimarting?ales. The equation discussed in this paper unifies the equations in papers [1, 2]. This paper gives us the sufficient conditions for the existence and uniqueness of its solutions, so that the results in papers [1,2] can be obtained by theorem 1 and theorem 1; of this paper respectively.     

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO NONLINEAR DELAY FRACTIONAL DIFFERENTIAL EQUATIONS

Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.