一阶中立型微分差分方程解的振动性质

在本文中我们研究中立型微分差分方程d/dt[x(t)+sum from i=1 to m(p_ix(t-τ_i))]+sum from i=1 to n(Q_i(t)x(t-σ_i)=0,t≥t_0的解的振动性态。本文推广[1]的诸结果,同时改进[1]的定理3和定理4。     

具多滞量和正负系数中立型微分方程解的渐近性质

该文考虑多滞量和正负系数中立型方程[x(t)-sum from n=1 to l(1/n)C_A(t)x(t-r_n)] sum from i=1 to (1/i)P_i(t)x()t-τ_i)-sum from j=1 to n(1/j)Q_j(t)x(t-σ_j)=0,其中C_A(k=1,…,l),P_i(i=1,…,m),Q_j(j=1…,n)∈C([to,∞co),R~ ),0≤τ_l<…<τ_m,0≤σ_1<…<σ_n,0相似文献   

一类二阶泛函微分方程解的渐近性

对各类二阶微分方程解的性质,自1971年Hammett以来已有许多讨论,如[1]—[10]本文讨论二阶时滞泛函微分方程 (r(t)x′(t))′+sum from i=0 to n (P_i(t)g_i′(x(t-τ_i(t))))+sum from i=0 to n (q_i(t)g_i(x(t-τ_i(t))))=f(t) (1)的解的渐近性质,其中;r(t)、q_i(t)、g_i(x)、τ_i(t)、f(t)连续;p_i(t)连续可微;当p_i(t)不恒为0时,g_i(x)连续可微;当x≠0,xg_i(x)>0;g_i(x)关于x单调不减;F(u)=integral from n=to to u (|f(s)|ds)<∞;g_0(x)=x,τ_0(t)=0。     

一类三阶泛函微分方程周期解的存在唯一性

利用重合度理论研究了一类三阶泛函微分方程x′′′(t)+multiply from i=1 to 2[a_ix~((i))+b_ix~((i))(t-τ_i)]+ g_1(x(t))+g_2(x(t-τ))=p(t)的2π-周期解问题,获得了该方程2π-周期解存在唯一性的若干新结论.     

A NECESSARY AND SUFFICIENT CONDITION FOR THE OSCILLATION OF HIGHER-ORDER NEUTRAL EQUATIONS WITH SEVERAL DELAYS

Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots.     

稳定性参数区域之进一步估计

在[1]中,笔者用标量函数的方法研究了具有分解形式(dX_i)/(dt)=G_i(X_i,t) sum from i=1 j(?)i to r A_(ij)(t)X_j(t) sum from j=1 to r B_(ij)(t)[X_j(t-τ(ij))-X_j(t)](i=1,2,…,r)的复合系统(dX)/(dt)=H[t,X(t),X(t-τ)]及具有分解形式     

关于线性偏差变元微分方程的振动性

本文讨论了变时滞非自治微分方程 x~′(t)+sum from i=1 to n p_i(t)x(t-τ_i(t))=0的解的振动性,建立了一些振动判据,并改进了文[1]的主要结果.     

一类非线性微分-差分方程解的殆指数渐近稳定性

对形如 x(t)=af(x(t))+ sum from i=1 to n (b_if_i(x(t-τ_i)))的微分-差分方程,给出了其零解殆指数渐近稳定的定义,得到了几个判定零解殆指数渐近稳定性的定理。     

关于线性偏差变元微分方程解的振动准则

本文讨论了线性非自治时滞微分方程 x′(t)+sum from i=1 to n(p_i(t)x(t-τ_i(t)))=0的解的振动性,推广和改进了Ladas等人的主要结果。     

非参数回归函数的基于截尾数据的估计

本文考虑截尾数据情况下非参数回归函数m(x)=E(Y|x)的估计。具体地讲,我们面对的是这样的数学模型:T是与(X,Y)独立的随机变量,我们观测到的不是Y本身,而是Z=min(Y,T)及δ=[Y≤T]。今有训练样本{(X_i,Z_i,δ_i)}_(i-1)及当前样本(X,z,δ),记ξ_i(·)=[z_i≥·], N~ (·)=sum from i=1 to n ξ_i(·), V_n(·)=multiply from i=1 to n{1 N~ (z_i)/2 N~ (z_i)}~[δ_i=_i<0], U_n(·)=sum from i=1 to n Wnt(x)ξ_i(·), 令 m_n(x)=integral from 0 to u_n U_n(y)|V_n(y)dy, 其中u_n=F_2~(-1)(n~(-a)),0<α<1/2为一实常数,F_2(·)=P(Y≥·)为Y的(右侧)分布函数。在权函数{W_(ni)(x)}_(i=1)~n及(X,Y,T)的分布函数满足一组条件下,我们证明了m_n(x)为m(x)的强相合估计,即:m_n(x)→m(x),a.s.(n→ ∞).     

变系数高阶中立型微分方程的振动性

考虑变系数高阶中立型微分方程(NDDE)d~n/(dt~n)[y(t)+p(t)y(t-τ)]+sum from n=1 to ∞q~i(t)y(t-σ_i)=0 (1)其中p(t)、g_i(t)都是区间[T,∞)上连续的实值函数.p(t)有界,q_i(t)≥0(i=1,2,···,m)且至少有一个q_i(t)最终大于某一任意小的正数.τ≥0,σ_i≥0.m≥1,n≥1均为正整数. 本文研究了方程(1)在p(t)≥一1及p(t)≤-1等情况下解的渐近性和振动性,获得了一系列使解振动的充分条件.特别,p(t)有时可以是变号函数.     

二阶非线性中立型时滞微分方程的振动性

考虑二阶非线性中立型时滞微分方程(x(t)-p(t)x(t-τ))″+∑ from i=1 to n (qi(t)fi(x(t-σi)))=0,t0,其中p,q_i∈C(R+,R+),τ,σ_i∈(0,∞),f_i∈C(R,R),i=1,2,…,n,分别得到了方程所有解振动和方程存在非振动解的充分条件,推广和改进了相关文献中的相关结果.     

Richard模型的平均期望费用问题

设 W_t,t≥0为(Ω,■,P)上标准 Wiener 过程,■为由之所生成的上升 σ-域族,以τ_i,i≥1表任一个(?)单调上升停时列,对每个τ_i 确定一个F_(τi)可测随机变量ξ_i,我们称任一这样的对列 v={(τ_i,ξ_i),i≥1}为一脉冲过程,以 V 表脉冲过程,(以下称脉冲控制)的全体,设 h 和 B 为 R 上满足某些条件的非负实函数,再设σ,μ为任何实常数且|σ|>0.本文求得一个常数λ>0使对任一实数 x 皆有一个十分明确具体的控制 v~*={(τ_i~*,ξ_i~*),i≥1)∈V 满足lim~T→∞(1/T)E[integral from 0 to T h(x+μt+σW_t+sum τ_i~*相似文献   

三阶泛函微分方程的周期解

利用Brouwer度理论得到了泛函微分方程x′″（t） ∑i=0^2[αix(i)(t) bix(i)(t-τi)] g1(x(t)) g2(x(t-τ））=p（t）存在2π周期解的充分性条件，推广了[1]中的有关结果．     

OSCILLATIONS OF NEUTRAL DIFFERENTIAL DIFFERENCE EQUATIONS

Recently the authors have studied the oscillations of some neutral differential difference equations and obtained very good results (see [1—4]). In this paper we consider the oscillations of the neutral differential difference equationd/dt[x(t)+sum from i=1 px(t-τ)+sum form j=1 to n qx(t-σ)=0, t≥t,] (*)where p, τ, q and σ (i=1, 2, …, m; j=1, 2, …, n) are positive constants. Some sufficient conditions for all solutions of (*) to oscillate are obtained. And in some ease we give neeessaxy and sufficient conditions for (*) to oscillate.     

OSCILLATORY AND ASYMPTOTIC BEHAVIORS OF FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper the author discusses the following first order functional differentialequations: x'(t) +integral from n=a to b p(t, ξ)x[g(t, ξ)]dσ(ξ)=0, (1) x'(t) +integral from n=a to b f(t, ξ, x[g(t, ξ)])dσ(ξ)=0. (2)Some suffcient conditions of oscillation and nonoseillafion are obtained, and two asymptolioproperties and their criteria are given. These criferia are better than those in [1, 2], and canbe used to the following equations: x'(t) + sum from i=1 to n p_i(t)x[g_i(t)] =0, (3) x'(t) + sum from i=1 to n f_i(t, x[g_i(t)] =0. (4)     

共振条件下多点边值问题解的存在性

本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.     

Strong approximation of empirical process with independent but non-identically distributed random variables

Let{Y_t,t=1,2,…} be independent random variables with continuous distribution functionsF_i(y).For any y,dencte s=F_t(y)=1/t sum from i=1 to t F_i(y).The empirical process is defind by t~(-1/2)R(s,t) whereR(s,t)=t(1/t sum from i=1 to t I_((?)_t(Y_i)≤s)-s)=sum from i=1 to t I_(?)-ts=sum from i=1 to t I_(?)-(?)_t(y)=sum from i=1 to t I_(Y_(?)≤y)-sum from i=1 to t F_i(y).The purpose of this paper is to investigate the asymptotic properties of the empirical processR(s,t).We shall prove that for some integer sequence {t_k},there is a (?)-process (?)(s,t) such that(?)|R(s,t_k)-(?)(s,t_k)|=O(t_k~(1/2)(log t_k)~(-1/4)(log log t_k)~(1/2))a.s.where (?)(s,t) is a two-parameter Gaussian process defined in §1.     

正实部解折函数的渐近性质

一 引言 令表示P(z)在U:|z|<1内正则P(0)=1,且ReP(z)>0的函数全体。中两函数P_1,P_2的Hadamard乘积定义为 (P_1*P_2)(z)=1+1/2sum from n=1 to ∞(C_n~(1)C_n~(2)z~n) 其中 P_i(z)=1+sum from n=1 to ∞(C_n~(i)z~n∈记P(z)=1+sum from n=1 to ∞C_nz~n。 本文主要研究P(z)的渐近性质,最后说明其在单时函数论中的应用。二 几条引理     

一类非线性Volterra积分微分方程组及褶积型积分方程组的解之延展和界值

对非线性Volterra型积分微分方程组x'(t)=f(t,x(t))+sum from j=1 to m(integral from n=0 to t(A_j(t,s)g_j(s,x(s))ds)),t∈R_+ (1)以及褶积型积分方程组y(t)=F(t)+sum from j=1 to m(integral from n=0 to t(B_j(t-s)G_j(s,y(s))ds)),t∈R_+ (2)我们得到了如下结果:定理1 若方程组(1)满足下列条件1)f(t,η),g_j(t,η)∈c[R_+×R~n,R_n],A_j(t,s)∈c[R_+×R_+,R~(n×n)],它们使得(1)