Liénard方程极限环存在定理

讨论了非线性振动方程:(x:)+f(x)(x.)+g(x)=0在G(±∞)=+∞的限制被取消时,其极限环的存在性.     

STATIONARY SOLUTION FOR A STOCHASTIC LI(E)NARD EQUATION WITH MARKOVIAN SWITCHING

This paper considers a stochastic Lienard equation with Markovian switching.The Feller continuity of its solution is proved by the coupling method and a truncation argument. The existence of a stationary solution for the equation is also proved under the Foster-Lyapunov drift condition.     

一类具时滞变量的类p-Laplacian Liénard微分方程周期解的存在性

本文研究了一类具类p-Laplacian项Liénard微分方程.应用广义Borsuk定理,在系数c(t)为非常值函数的情况下,得到了该方程周期解存在性的一个新的结果.

Abstract：

In this article,we study a kind of p-Laplacian-like Liénard differential equation.By using the generalized Borsuk theorem in coincidence degree theory,a new result on the existence of its periodic solution is obtained in the case that the cofficient c(t)is not a constant function.     

THE UNIQUENESS OF LIMIT CYCLE AND CRITICAL POINT FOR A CLASS OF CUBIC SYSTEM

In this paper,we consider an accompany system concerning some class of cubic system. We then prove that the system has at most one limit cycle. Finally,we obtain the topological structure of both the critical points at infinity and the singular points lying on invariant lines.     

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.     

具有临界和非临界操作错误的人机系统的渐近稳定性

讨论具有临界和非临界操作错误的可修复人机系统．利用系统算子生成的Banach 空间中的正压缩C0半群的性质,证明了此系统的唯一非负时间依赖解恰是系统算子0本征值对应的规范化后的本征向量;同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的一个直接结果,得出了该可修人机系统的渐近稳定性．     

广义 Liénard 方程的整体渐近性态

我们研究如下的广义 Liénard 方程的整体渐近性态(?)+f(x)(?)+g(x)=e(t),或等价地,(?)其中,f(x),g(x)是实数轴上的连续函数,e(t)为正半轴上的连续函数.     

具有幂零奇点的七次Hamilton系统Abel积分的零点个数估计

本文研究了具有幂零奇点的七次Hamilton系统的Abel积分的零点个数问题.利用Picard-Fuchs方程法,得到了Abel积分I(h)=∮_(Γh)g(x,y)dx-f(x,y)dy在(0,1/4)上零点个数B(n≤3[(n-1)/4]),其中Γ_h是H(x,y)=x~4+y~4-x~8=h,h∈(0,1/4),所定义的卵形线f(x,y)=∑(1≤4i+4j+1≤n)aijx~(4i+1)y~4j)和g(x,y)=∑(1≤4i+4j+1≤n)bijx~4iy~(4j+1)是x和y的次数不超过n的多项式.     

具有二阶细焦点的二次系统极限环的唯一性

人们猜想,平面二次系统二阶细焦点外围至多存在一个极限环,但迄今未能证实.文[1,2]在某些参数取特定值之下证明了这一猜想.最近文[5]在具有零特征根奇点之下也证明了这一猜想.本文则在较一般的情况下证明了这一猜想,并使文[5]的结果成为本文的特例.此外,本文还给出了若干有环无环的条件.     

THE LOCAL CENTER OF GENERALIZED LIENARD SYSTEM

This paper gives a theorem for the local center of generalized Lienard system; the relative theorems in the references can be deduced from our corollaries.     

ON THE CENTER OF GENERALIZED LIENARD SYSTEM

This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.     

一类具有相同对称/反对称中心的正交平衡向量小波系统的不存在性

本文得到两个结果:首先证明尺度因子m与重数r的乘积为奇数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)(μ∈N)的正交向量小波系统的不存在性;其次证明尺度因子m=3,重数r为偶数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)的正交平衡向量小波系统的不存在性,这里N是正整数集合.     

LIMIT CYCLES FOR A CLASS OF E_3~1 SYSTEMWITH A FINE FOCUS AND A FINE SADDLE

1IntroductionManypracticalproblems,suchasnon--linearvibration,reactionofbiochemistrygandself-oscillatingsystem,etc.canbereducedtotheproblemsonthelimitcyclesofEjsystem.Therefore,thestudyoflimitcyclesforEjsystemhaspracticalsignificances.ThesocalledEdsystemi…     

对称中心相同的正交平衡多小波的存在性及参数化

1 引 言 多小波因为可同时满足对称性、紧支撑性、高阶消失矩和正交性,所以在信号处理等应用方面比单小波更有优势,但是,基于多小波的信号处理需进行预滤波[1,2],而预滤波又会破坏所设计的多小波的正交性、对称性等特性,这阻碍了多小波的应用.     

PHASE-PORTRAIT OF A CERTAIN INTEGRABLE QUADRATIC DIFFERENTIAL SYSTEM WITH CENTER

In [1] we have proved that the quadratic differential system:has a center O(0, 0), which satisfies the last conditions of [2] 512 Theorem 12.3:Aside from O, (1) has a second finite critical point N(0, 1/n), it is an unstablenode. In [3], this is the case (7) in P.16, with bifurcation curve C12 in Fig.4.1and phase-portrait V32 in P.11.Now, put n = I, thenand (l) becomes:From [1] we know that (4) has a quadratic algebraic integral curveIt is a non--degenerate parabola with symetrical axis x…     

多项式判别矩阵的若干性质及其应用

具有文字系数的多项式f(x)，其判别矩阵是f与f′的Sylvester矩阵通过添加一行一列而得，已经知道，判别矩阵的偶数阶主子式的符号确定了f(x)的相异根(实根、复根)的数目，这里介绍如何将奇数阶与偶数阶主子式相结合用以判定该多项式的相异负根或正根的数目，并进一步判定其在区间上的实根数，本文还研究了与判别矩阵相关的一些实用性质，并应用这些性质给出了4次键合多项式不能正分解的一组简洁的充分必要条件。     

LIMIT CYCLES OF CUBIC VAN DER POL EQUATION WITH ONE FINITE CRITICALPOINT

ItiswellknownthatavarietyofsignificantpracticalproblemsleadtoVanderPciequation'Equation(l)canalsobewritteninitsequivalentformItisacubicdifferentialsystemiff(x,y)y h(x)isacubicpolynomial,correspondingly,equation(1)issaidtobecubicVanderPciequation.Inthispap…     

一类具有多偏差变元的Liénard系统的反周期解

研究了一类具有多偏差变元的Liénard系统的反周期解,获得了该系统反周期解的存在性与全局指数稳定性的新充分条件.     

ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS

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