线性常微分方程组稳定性的代数判据

本文首先证明多项式无正实部零点的充要条件;其次,得到线性常微分方程组稳定性的斯的充要条件;最后给出几类特殊系统稳定的简便的充分条件。     

常微分方程组积分因子存在的充要条件

给出并证明了自治和非自治常微分方程组积分因子存在的充要条件,从而给出当常微分方程组的向量场散度不为零时的构造积分因子的方法。     

几类三阶非线性常微分方程组边值问题正解的存在性

研究几类二阶非线性常微分方程组的边值问题,在合适的条件下,利用锥拉伸不动点定理获得了其正解的存在性.     

某类常微分方程组的特征值不等式

本推导出某类二阶线性常微分方程组的特征值不等式，利用前n个特征值来估计出第n 1个特征值的上界，其估计不依赖于区间的几何度量。     

几种微分方程李对称决定组生成软件包的比较研究

根据微分方程李对称决定方程组生成算法,在计算机代数系统Maple上给出了具体实现GDS,并指出了现行Maple系统上关于李对称计算的软件包liesymm的缺陷,最后通过一些计算实例对三个Maple系统下的软件包GDS,liesymm以及Desolv进行了比较研究.     

拟线性常微分方程组边值问题解的估计

本文研究拟线性常微分方程组边值问题x′=f(t,x,y,ε),x(0,ε)=A(ε) εy″=g(t,x,y,ε)y′+h(t,x,y,ε) y(0,ε)=B(ε),y(1,ε)=C(ε)的奇摄动。其中x,f,y,h,A,B和C均属于Rn,g是n×n矩阵函数。在适当的条件下,利用对角化技巧和不动点定理证明解的存在,并估计了余项.     

对称群在面饰分类中的应用(续)

（1）对称群的生成元只含有两个平移．此时生成关系唯一确定：tαtb=tbtα。 图示如下：     

高阶非线性常微分方程组周期解的存在性

本文考虑非线性常微分方程组周期解的存在性,得到了周期解的Ｎａｇｕｍｏ型先验估计,由此在一般性条件下证明了方程组至少有一个Ｔ－周期解,     

THE LIE ALGEBRA ADMITTED BY ANORDINARY DIFFERENTIAL EQUATION SYSTEM

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｉｔｗｉｌｂｅｓｈｏｗｎｔｈａｔ，ｔｈｅｓｐａｃｅｇｅｎｅｒａｔｅｄｂｙａｌｇｅｎｅｒａｔｏｒｓｏｆｏｎｅｐａｒａｍｅｔｅｒＬｉｅｇｒｏｕｐｓａｄｍｉｔｅｄｂｙａｎｇｉｖｅｎｏｒｄｉｎａｒｙｄｉｆ...     

LIE GROUPS ADMITTED BY AUTONOMOUS SYSTEM WITH GIVEN STRUCTURE CONSTANTS

1IlltroductionandNotationsInthesecondhalfofthepreviouscentury,SophousLieintroducedthetheoryofLiegroups,inordertocreateatheoryofintegratingordinarydifferentialequations.Sofar,Liegrouptheoryhadplayedimportantimpactinintegrabilitytheoryofdifferentialequations(ref.[l,2,3]).Considerthefollowingfirstorderautonomoussystemofnordinarydifferentialequations'wherex=(x',x',''3x)ED,andDisasub-domainofR(orC),XifD-- R(orC),XfECoo(D),andtER(orC).Astheclassicalresult,theorderofthesystemcanbereduced…     

双比例延迟微分方程配置法的可达阶

近几十年来,随着延迟微分方程广泛应用于变最测试、信号传递、机械化工、生命科学及经济管理系统等实际中,人们对此类方程的数值计算要求越来越高．     

ON THE BOUNDEDNESS OF A CERTAIN SYSTEM OF FIFTH-ORDER DIFFERENTIAL EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｓｈａｌｂｅｃｏｎｃｅｒｎｅｄｈｅｒｅｗｉｔｈｒｅａｌｆｉｆｔｈｏｒｄｅｒｖｅｃｔｏｒｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｔｈｅｆｏｒｍ：Ｘ（５）＋Ｆ（Ｘ．．）Ｘ（４）＋Φ（Ｘ．．）＋Ｇ（Ｘ．．）＋Ｈ（Ｘ．）＋Ψ...     

A ONE-STEP EXPLICIT FORMULA FOR THE NUMERICAL SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATION*

In this paper, a new one-step explicit method of fourth order is derived. The new method is proved to be A-stable and L-stable, and it gives exact results when applied to the test equation y'=λy with Re(λ)<0, Also several numerical examples are included.     

A SINGULAR BOUNDARY VALUE PROBLEMFROM DRAINING AND COATING FLOWSINVOLVING A THIRD-ORDER ORDINARY DIFFERENTIAL EQUATION

1IntroductionInarecentsurveypaperTuckandSchwarts[3]discussedaseriesofthird-orderordinarydifferentialequationsarisinginthestudyoftheflowofathinfilmofviscousfluidoverasolidsurface.Whensuchafilmdrainsdownaverticalwallandtheeffectsofsurfacetensionandgravityaswellasviscosityaretakenintoaccount,oneisledtoanequationoftheformforthefilmprofiley(x)inacoordinateframemovingwiththefluid.Herethex--axisischosentobepointingupwords.Generallyspeaking,thefunctionf(y)issingularaty=0,thatis,atthetipofthefilm.Its…     

一类分数阶常微分方程初值问题的预校算法

利用Caputo导数的性质和二次多项式插值逼近,导出了分数阶二次多项式插值逼近隐式算法的完整计算公式,证明了其整体误差估计为O(hβ),β=min{2+α,3};在此基础上,构造了一类求解分数阶常微分方程初值问题的新的预校算法, 证明了其整体误差估计为 O(hγ),γ=min{2α,2+α,3},并通过数值实例得以验证.     

A NEW OSCILLATION CRITERION FOR FIRST ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION

In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.     

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.