中立型标量积分微分方程的周期解

本文考虑中立型标量方程x′(t)=a(t)x(t)+∫     

具时滞的高维周期系统周期解的存在性与唯一性

本文考虑了具时滞的高维周期系统x’(t)=A(t,x(t))x(t)+f(t,x(t-r)),其中(t,x)∈R×R~n,A(t,x)是n×n连续矩阵,f(t,x)是n维连续向量,且A(t+T,x)=A(T,x),f(t十T,x)=f(t,x).利用不动点方法,建立了保证其T周期解的存在性及唯一性的充分条件.所得结果推广、改进了文[1-3]的主要结果.     

一类Green函数变号的二阶两点边值问题正解的存在性

讨论了Green函数变号的二阶两点边值问题：其中f：[0,1]×[0,＋∞）→[0,＋∞）连续.利用Guo-Krasnosel＇skii不动点定理得到了正解的存在性.     

一类积分微分方程周期解的存在性和唯一性

本文考虑具连续时滞和离散时滞的非线性积分微分方程x'(t)=A(t,x(t))x(t)+∫-∞tC(t,s)x(s)ds+∑i=1i gi(t,x(t—τi(t)))+b(t)和x’(t)=f(t,x(t))+∫-∞tC(t,s)x(s)ds+∑i=1igi(t,x(t-τi(t)))+b(t)周期解的存在性和唯一性问题,这里t∈R,x∈Rn;A(t,x),C(t,s)为n×n阶连续的函数矩阵; f(t,x),gi(t,x)(i=1,2,…,l),b(t)是n维连续向量.通过利用线性系统指数型二分性理论和泛函分析方法研究上述系统,获得了保证其周期解存在性、唯一性的充分性条件.我们除了实质性的推广和改进了已有的结果外,还得到三个新的定理,这是用已有的方法无法获得的(见文[1-30]).     

Asymptotic Behavior of Solutions of Some Linear Difference Equations with Oscillatory Decreasing Coefficients

We investigate the asymptotic behavior of solutions of the system x ( n +1)=[ A + B ( n ) V ( n )+ R ( n )] x ( n ), n S n 0 , where A is an invertible m 2 m matrix with real eigenvalues, B ( n )= ~ j =1 r B j e i u j n , u j are real and u j p ~ (1+2 M ) for any M ] Z , B j are constant m 2 m matrices, the matrix V ( n ) satisfies V ( n ) M 0 as n M X , ~ n =0 X Á V ( n +1) m V ( n ) Á < X , ~ n =0 X Á V ( n ) Á 2 < X , and ~ n =0 X Á R ( n ) Á < X . If AV ( n )= V ( n ) A , then we show that the original system is asymptotically equivalent to a system x ( n +1)=[ A + B 0 V ( n )+ R 1 ( n )] x ( n ), where B 0 is a constant matrix and ~ n =0 X Á R 1 ( n ) Á < X . From this, it is possible to deduce the asymptotic behavior of solutions as n M X . We illustrate our method by investigating the asymptotic behavior of solutions of x 1 ( n +2) m 2(cos f 1 ) x 1 ( n +1)+ x 1 ( n )+ a sin n f n g x 2 ( n )=0 x 2 ( n +2) m 2(cos f 2 ) x 2 ( n +1)+ x 2 ( n )+ b sin n f n g x 1 ( n )=0 , where 0< f 1 , f 2 < ~ , 1/2< g h 1, f 1 p f 2 , and 0< f <2 ~ .     

一类非线性中立型脉冲时滞微分方程解的渐近性

该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件.     

Superoptimal Preconditioners for Functions of Matrices

For any given matrix $A∈\mathbb{C}^{n×n}$, a preconditioner $t_U(A)$ called the superoptimal preconditioner was proposed in 1992 by Tyrtyshnikov. It has been shown that $t_U(A)$ is an efficient preconditioner for solving various structured systems, for instance, Toeplitz-like systems. In this paper, we construct the superoptimal preconditioners for different functions of matrices. Let $f$ be a function of matrices from$\mathbb{C}^{n×n}$ to$\mathbb{C}^{n×n}$. For any $A∈\mathbb{C}^{n×n}$, one may construct two superoptimal preconditioners for $f(A)$: $t_U(f(A))$ and $f(t_U(A))$. We establish basic properties of $t_U(f(A))$) and $f(t_U(A))$ for different functions of matrices. Some numerical tests demonstrate that the proposed preconditioners are very efficient for solving the system $f(A)x=b$.     

二元非乘积型Baskakov算子的某些逼近性质

该文利用多元分解技巧及一元的结果得出二元非乘积型算子V\-n的两个逼近性质定理.对f∈C\-0(T\+2),‖V\-n(f)-f‖≤cω\-2(f,[SX(]1[]n[SX)]); 对f∈C\+2(T\+2),lim[DD(X]n→∞[DD)]n(V\-n(f)-f)=[SX(]x(1+x)[]2[SX)]f\-\{11\}+[SX(]y(1+y)[]2[SX)]f\-\{22\}+[SX(]xy[]2[SX)]f\-\{12\}.     

Maximal inequalities for a continuous semimartingale

Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 .     

一类中立型高维周期微分系统的周期解

本文考虑中立型高维周期系统：其中（L,x）∈R×R~n,A（t,x）为连续函数矩阵,x_t∈C（[-γ,0],R~n）,x_t（θ）＝x（t十θ）,θ∈[-r,0],记C＝C（[-r,0］,R~n）,f：R×C→R~n连续,且A（t＋T,X）＝A（t,x）,T,r＞c∈R,本文用不动点方法研究此系统,得到了其周期解存在的充分性条件,所得结果推广、改进了文［1－3］中相应结论．     

具无限时滞的非线性积分微分方程的周期解

本文考虑具无限时滞非线性积分微分方程和其中t∈R,T≥0是常数,x∈Rn;A(t,x),C(t,s)为n×n连续的函数矩阵;f(t,x),g(t,x),b(t)是n维连续向量.本文利用线性系统的指数型二分性理论和不动点定理研究此系统,建立了保证其周期解存在性.唯一性的充分条件.得到了一些新的结果,推广了相关文献的主要结果.     

某些二阶系统正解的存在性

考察如下边值问题正解的存在性x″(t) λa(t) f (x(t) ,y(t) ) =0y″(t) λb(t) g(x(t) ,y(t) ) =0x(0 ) =x(1 ) =y(0 ) =y(1 ) =0其中 f ,g:R × R R ;a,b:[0 ,1 ] R .所有的函数都被假定是连续的 ,此外 f ,g满足某些增长性条件 .本文得到了一些正解的存在性结果 .     

Hermite-Fejér插值算子的一个渐近估计式

设f(x)在[-1,1]上的二阶导数存在且有界,H_n[f(t);x]、R_n[f(t);x]分别为具有第一类、第二类零点的Hermite-Fejér插值多项式,则当n→∞时,有 H_n[f(t);x]-f(x)=O(1/n)(-1相似文献   

Oscillatory and Asymptotic Behavior of First Order Functional Differential Equations

In this paper the author discusses the following first order functional differential equations: $x''(t)+[\int_a^b {p(t,\xi )x[g(t,\xi )]d\sigma (\xi ) = 0} \] (1)$ $x''(t)+[\int_a^b {f(t,\xi )x[g(t,\xi )]d\sigma (\xi ) = 0} \] (2)$ Some sufficient conditions of oscillation and nonoscillation are obtained, and two asymptotic properties and their criteria are given. These criteria are better than those in [1, 2], and can be used to the following equations: $x''(t)+[\sum\limits_{i = 1}^n {{p_i}(t)x[{g_i}(t)] = 0} \] (3)$ $x''(t)+[\sum\limits_{i = 1}^n {{f_i}(t)x[{g_i}(t)] = 0} \] (4)$     

非线性项依赖于一阶导数的共振情形下二阶三点边值问题解的存在性和唯一性

本文致力于研究共振情形下二阶三点边值问题x″(t)+ f(t,x(t),x'(t))=0, t∈(0,1),x(0)=0, x(1)=ξx(η),其中f:[0,1]×R2→R是一个连续函数,ξ＞0,0＜η＜1满足ξn=1.运用先验界估计,微分不等式技巧和Leray-Schauder度理论得到了该边值问题解的存在性和唯一性.     

高阶泛函微分方程解的渐近分类与振动

本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程解的渐近分类与振动性。     

Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理

研究了Lipschitz伪压缩映射的黏滞迭代方法.设E为一致光滑Bannach空间,K为E的闭凸子集,TK→K为Lipschitz伪压缩映射且其不动点集F(T)非空,f为K上的压缩映射且t∈(0,1).若黏滞迭代路径{xt},xt=(1-t)f(xt) tTxt且对任意初始向量x1∈K,迭代序列{xn}定义为xn 1=λnθnf(xn) [1-λn(1 θn)]xn λnTxn,则当t→1-和n→∞时,{xt}和{xn}都强收敛于T的不动点,同时该不动点还是一类变分不等式的解.     

矩阵多项式空间的进一步研究

设A为数域F上的n级矩阵,记F[A]={f(A)|f(x)∈F[x]},它显然是F~(n×n)的子空间.讨论了F[A]的基和维数,引入了f(A)的坐标和F[A]的因式子空间的概念,给出了用因式子空间表示F[A]的几个定理,刻画了F[A]的结构.     

具非线性边界条件的Volterra型时滞微分方程边值问题奇摄动

该文研究一类时滞微分方程边值问题〖JB({〗εx″(t)=f(t,x(t),x(t-τ(t)),\[Tx\](t),x′(t),ε),t∈(0,1),\=x(t)=φ(t,ε),t∈\[-τ,0\],h(x(1),x′(1),ε)=A(ε),[JB)]其中ε>0为小参数，τ(t)≥τ\-0>0,τ=\%\{max\}\%[DD(X]t∈\[0,1\][DD)]τ(t)<1,\[Tx\](t)=ψ(t)+∫\+t\-0k(t,x)x(s）ds为Volterra型算子。利用微分不等式理论证明了边值问题解的存在性，并给出了解的一 致有效渐近展开式。     

带有阻尼项的偏泛函微分方程解的振动性

本文研究带有阻尼项的双曲型时滞偏微分方程 2 t2 u(x,t) +m(t) u t=a(t)△ u(x,t) +b(t)△ u(x,ρ(t) ) -q(t) f (u(x,σ(t) ) ,(x,t)∈ G≡Ω× R+ (1 )其中 ,R+=[0 ,+∞ ) ,Ω是一个具有逐段光滑边界的有界区域 .利用平均法和微分不等式方法得到方程 (1 )的若干新的振动准则 .