THE STABILITY OF RDDE (?)(t) p_1(t)x(t) q_1(t)x(t) p_2(t)x(t-r(t)) q_2(t)x(t-r(t))=0

In this paper, the author considered the stability of zero solution of linear RDDEx(t) p_1(t)x(t) q_1(t)x(t) p_2(t)x(t-r(t)) q_2(t)x(t-r(t))=0,(1)x(t) p_1(t)x(t) q_1(t)x(t) q_2(t)x(t-r(t))=0 (2)using Liapunov-Razumikhin functional and transformations and obtained some sufficient condi-tions for the stability of Eqs.(1) and (2). These results are suitable both for bounded p_i(t), q_i(t)and r(t).i =1, 2.     

On the Cauchy problem for D t 2–D x a(t,x) n D x

Abstract The well posedness of the Cauchy problem for the operator P=D_t²–D_xa(t,x)ⁿD_x, with data on t=0 is studied assuming a ∈ C^N( (R)), s₀>1 and sufficiently close to 1, a(t,x)≥ 0. Well posedness is proved in Gevrey classes γ^(s), for , n≥ n₀. Keywords: Partial differential equations, Cauchy problem, Well posedness     

The Existence of a Positive Solution of D α[x(t) − x(0)] = x(t)f(t,x t )

This paper is devoted to the problem of existence of positive solution for a delay differential equation with fractional order. Some sufficient conditions for its existence of positive solution are given. This work was supported in part by the Key Project of the National Nature Science Foundation of China (No. 60534020), the National Nature Science Foundation of China (No. 60474037), and Program for New Century Excellent Talents in University (No. NCET-04-415).     

关于满足I(x,n(x))=n(x)的D-蕴涵的刻画

研究I(x,n(x))=n(x),其中I为由连续三角模T、连续三角余模S和强否定n生成的D-蕴涵,即I(x,y)=S(T(n(x),n(y)),y),给出了满足I(x,n(x))=n(x)的充要条件。     

方程(t)+p(t)(t)+q(t)x(t)=0的稳定性

本文应用交换技巧以及直接方法研究了二阶线性系统(1)的平凡解的稳定性,得到若干充分条件、必要条件以及充分必要条件,推广了文献[1—8]中的有关结果。     

2π-PERIODIC SOLUTION OF THE EQUATION x + f(x)x + bx + g(x(t - т)) = p(t)

In this paper, time delay Lienard's equations are considered, by using the theory of concidence degree, a sufficient condition of existence of at least one 2π-periodic solution is obtained.     

On the recursive sequencex n +1=α-(x n /x n −1)

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n + 1} = \alpha - \frac{{x_n }}{{x_{n - 1} }}, n = 0,1,...,$$ where α∈R is a real number, and the initial conditionsx?1,x ₀ are arbitrary real numbers.     

Contributi allo studio asintotico dell'equazionex‴(t) +p(t)x(t)=0

Sunto è contenuto nel n. 1 della Memoria. A Giovanni Sansone nel suo 70^mo compleanno.     

关于Diophantine方程(20n)x+(21n)y=(29n)z

设a,b,c是满足条件a2+ b2=c2的两两互素的正整数.Jesmanowicz于1956年猜想对于任意给定的正整数n,方程(an)x+(bn)y=(cn)z仅有解(x,y,z)=(2,2,2).本文证明了方程(20n)x+(21n)y=(29n)z有唯一解(x,y,z)=(2,2,2).     

One-Sided Boundary Control for the Process of Oscillations Described by the Equation k(x)[k(x)u x (x,t)] x − u tt (x,t) = 0

This article concerns the boundary control on the side x = 0 when the other side x = l is fixed. The corresponding process of oscillations is studied for the time interval T > 0 and is described by the generalized solution of the equation

方程组x=f(t,x)解的一致稳定性

本文给出了方程组x=f(t,x)解的一致稳定性的一个判别准则,改进了文献[1]中的有关结果。     

迭代微分方程x'(t)=ω(t)(ax(t)-bx(x(t)))(a>b>0)的周期解

本文讨论了一类非自治迭代微分方程ｘ’（ｔ）＝ω（ｔ）（ａｘ（ｔ）－ｂｘ（ｘ（ｔ）））（ａ＞ｂ＞０）的解的存在性、解的性态及周期．此结论推广了文［１］的定理．     

二阶线性方程(t)+p(t)(t)+q(t)x(t)=0一致稳定的一个充分条件

研究了二阶非定常线性微分方程的稳定性,利用分析技巧、Bellman不等式及稳定性有关理论得到了该方程一致稳定的一个充分性条件,获得了新的结论.     

x′=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分

本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广(参见文[1-12]).     

关于t(n)、F(m,n)分布数字特征的计算

在统计推断中，需用统计量来估计未知参数θ或ｇ（θ）的数值，如要进一步分析一个估计量的好坏，就需知道估计量的分布，或至少要知道统计量的某些数字特征．众所周知，ｔ统计量、Ｆ统计量在参数的点估计、区间估计、假设检验中起着重要的作用．文献［１］中介绍了几种重...     

方程 f(x,) g(x)=p(t)的周期解

在振动论、控制论等方面,方程 f(x,) g(x)=p(t)都有很重要的应用.早在四、五十年代N.Lavinson,C.E.Langenhop和G.Siefert等人对此方程周期解的存在性就进行了研究.本文引进了两个辅助方程,定义了半能量函数.引用了[3—6]中的“等零斜率曲线”得到了一些结果. 1.引理及定义对下列方程:     

N(t) = N(t) [a(t)-sum from i=1 to n (b_i(t)N~i(t-τ_i(t)))]的周期正解(英文)

用非线性分析的方法讨论了方程N（t）=N（t）[a（t）－bi（t）Ni（t-τ（t））周的周期正待的存在性，所获结果包含或推广了已有的几个结论[2，3]．