一类具有多个偏差变元的高阶中立型微分方程的周期解

利用Mawhin重合度理论,获得了一类具有多个偏差变元的高阶中立型微分方程(x(t)-cx(t-r))~(l)+h(x(t))x′(t)+■α~i(t)f(x′(t-μ_i(t))+■β_j(t)g(x(t-τ_i(t)))=p(t)周期解存在性的新结果,推广和改进了已有文献的相关结果.     

含有n个滞量的三维微分差分方程组周期解的存在性

本文研究含有n 个滞量的三维微分差分方程组x(t)=sum from i=1 to ∞(1/i)f[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]y(t)=sum from i=1 to ∞(1/i)g[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)](τ_i>0)z(t)=sum from i=1 to ∞(1/i)h[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]周期解的存在性,给出了方程组周期解周期的取值范围.推广并改进了文[1]的结果.     

一类时标上具状态依赖时滞的中立型泛函微分方程的周期正解

该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R~+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数.     

四阶p-Laplacian方程多时滞问题周期解的存在性

通过使用Mawhin连续性定理,研究四阶p-Laplacian微分方程多时滞问题(φ_p(x″(t)))″+f(t,x″(t))+(?)β_i(t)g(x(t-γ_i(t)))=p(t)周期解的存在性,并得到了存在周期解的充分性条件     

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   

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.     

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。     

SOLUTIONS TO A SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

This article deals with the following second-order multi-point boundary value problem x′′(t) = f(t,x(t),x′(t))+e(t),t ∈(0,1),x′(0)=(α_ix′(ξ_i) from i=1 to m,x(1)=(β_jx(ηj) from j=1 to n .Under the resonance conditions α_i from i=1 to m =1,β_j from j=1 to n=1,β_jηj from j=1 to n =1,by applying the coincidence degree theory,some existence results of the problem are established.The emphasis here is that the dimension of the linear operator is two.In this paper,we extend and improve some previously known results like the ones in the references.     

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.     

一类中立型时滞抛物偏微分方程的强迫振动性

研究了一类中立型时滞抛物偏微分方程:t(u(x,t)-pu(x,t-τ))-∑rk=1ak(t)Δu(x,t-ρk(t))+∑mj=1qj(t)u(x,t-σj(t))=e(x,t),的强迫振动性(其中(x,t)∈Ω×[0,∞)≡G,Ω是n维欧几里得空间Rn中带有逐段光滑边界Ω的有界区域,Δ是Rn中带有三类不同边值条件的拉普拉斯算子,强迫项e(x,t)是定义在G上的一个振荡函数),给出了一些新的振动性判据,这些结果推广了已知的一些结论.     

Solvability of a higher-order multi-point boundary value problem at resonance

Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance

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.     

On the Stability of Deformations of Cuntz–Toeplitz Algebras

Ukrainian Mathematical Journal - We study C*-algebras $$ {\mathcal{O}}_{n+m}^{\hat{q}} $$ generated by isometries $$ {\left\{{S}_i\right\}}_{i=1}^n\bigcup {\left\{{t}_j\right\}}_{j=1}^m, $$ where...     

方差分量模型中回归系数的线性Minimax估计

考虑方差分量(混合线性)模型y=Xβ+U1ξ1+U2ξ2+…+Ukξk,这里Xn×p,Ui,n×ti为已知设计矩阵,βp×1是固定效应,iξ是ti×1随机效应向量,满足E(iξ)=0,cov(iξ)=σ2iIti,iξ都不相关.往往Uk=In,ξk=ek,即最后一项为随机误差,热β∈RP和i2σ>0(i=1,2,…,k)为未知参数.我们考虑β的可估函数Sβ,选取二次损失函数L(d,Sβ)=(d-Sβ)′(d-Sβ)∑ki=1ciσi2+β′X′Vk-1Xβ,然后在线性估计类中给出Sβ的惟一的mini max估计.     

集值映射的不动点指数与带间断非线性项的椭圆型方程的多重解

<正> 本文研究二阶半线性椭圆边值问题■的多重解(符号详见§3),其中φ(x,t)允许对t是不连续的.一些自由边界问题可以化归这类问题.为了统一处理φ(x,t)对t连续与不连续两种情形,我们采用集值映射的观点.为此推广了经典的算子与Hammerstein算子到集值映射,并发展了集值映射的Leray-Schauder度理论;与已有的集值映射理论不同,现在处理的是映射串(定     

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.     

The Stability of Systems of Neutral Type with Small Time Lag

In this paper, we have obtained the equivalence theorems of stability between the system of differential equations $[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t)} (i = 1,2, \cdots ,n)\]$ and the system of differential-difference equations of neutral type $[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t - {\Delta _{ij}})} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t - {\Delta _{ij}})} (i = 1,2, \cdots ,n)\]$ where a_ij, b_ij, c_ij are given constants, and \Delta_ij are non-negative real constants.