Moser扭转定理在Lgrange稳定性中的应用

本文利用Moser扭转定理证明了一类Duffing方程x″+g(x)=e(t)的Lagrange稳定性,其中e(t)以1为周期,g:R→R具有下列性质:当x≥d0时,g(x)是超线性的;当x≤-d0时,9(x)是次线性的,其中d0悬一正常数.     

Lienard方程周期解、概周期解的存在性

本文考虑Lienard方程x“+f(x)x‘+g(x)=e(t),我们得到：当－∞＜infg‘(x)≤supg‘(x)&;lt;0且sups∈R|f(x)|&;lt;+∈∞时,对于任意周期或概周期函数e(t),它有周期或概周期解,而对于Lienard方程x“+f(x)x‘+cx=e(t),我们得到：当c&;gt;0且0&;lt;inf|f(x)|≤supx∈R|F(X)|&;lt;+∞时,对于任意周期或概周期函数e(t),它有周期或周期解。     

Lienard方程周期解、概周期解的存在性

本文考虑 Lienard方程 x″+f (x) x′+g(x) =e(t) ,我们得到 :当 -∞ 0且 0 相似文献   

具有非线性阻尼项和周期强迫项的次线性不对称可逆系统的拟周期解

本文考虑一类具有非线性阻尼项和周期强迫项的次线性不对称可逆系统x′′+α(x~+)~(1/3)-β(x~-)~(1/3)+q(x)g(x′)+f(x)=e(t)的Aubry-Mather集和拟周期解的存在性,其中x~±=max{±x,0},q(x)、g(x)和f(x)均是R上连续可微函数,e(t)是R上连续2π-周期函数.利用周修义(Shuinee Chow)和裴明亮建立的可逆系统的Aubry-Mather定理,在函数q(x)、f(x)和e(t)具有某种奇偶性假设条件下,本文证明了该可逆系统存在无穷多广义拟周期解.     

一类四阶抛物型方程的解的渐近行为

本文考虑一维空间中四阶抛物型方程Cauchy问题{ut-(e)2xu+(e)4xu=(e)xf(u), x∈R,t＞0,u(x,0)=u0(x), x∈R,的整体解u=u(x,t)的大时间渐近行为和时间衰减速率,其中f(u)∈C1(R), |f(u)|≤C|u|q, q＞5/2.     

多滞量非自治中立型泛函微分方程的(3)/(2)-渐近稳定性

考虑多滞量非自治中立型泛函微分方程(d)/(dt)x(t)-∑mi=1fi(t, x(t-τi))+∑nj=1gj(t,x(t-δj))=0, tt0,其中τi, δj∈(0,∞),fi, gj∈C([t0,∞)×R, R), i=1,2,...,m, j=1,2,...,n, 且当tt0,x∈R时,x*gj(t,x)0,j=1,2,...,n,获得了该方程零解一致稳定和渐近稳定的充分条件,推广并改进了现有文献中的相关结论.     

完全二阶常微分方程的奇周期解北大核心CSCD

本文讨论完全形式的二阶常微分方程-u"(t)=f(t,u(t),u’(t)),t∈R周期解的存在性,其中f:R^(3)→R连续,f(t,x,y)关于t以2π为周期.我们在非线性项f满足一些精准的不等式条件下,获得了方程奇2π-周期解的一些存在性结果.这些不等式条件允许f(t,x,y)当|(x,y)|→0及|(x,y)|→∞时关于(x,y)可以超线性或次线性增长.     

多滞量非自治中立型泛函微分方程的

考虑多滞量非自治中立型泛函微分方程(d)/(dt)x(t)-∑mi=1fi(t, x(t-τi))+∑nj=1gj(t,x(t-δj))=0, tt0,其中τi, δj∈(0,∞),fi, gj∈C([t0,∞)×R, R), i=1,2,...,m, j=1,2,...,n, 且当tt0,x∈R时,x*gj(t,x)0,j=1,2,...,n,获得了该方程零解一致稳定和渐近稳定的充分条件,推广并改进了现有文献中的相关结论.     

一阶非线性中立型泛函微分方程的振动性

近年来,关于一阶线性中立型泛函微分方程的振动性已有不少结果,但对于一阶非线性中立型泛函微分方程的振动性结果迄今很少见到。对下列的中立型泛函微分方程其中:P,τ,σ为正常数,Q(t),h(t)∈C[t_0,+∞),Q(t)>0,f(x)∈C(R,R),当x≠0时,Xf(x)>0。本文建立了振动性的两个结果。     

非线性微分系统解的有界性和周期解的存在性

本文运用了比较新的手法,证明了非线性微分系统(dx)/(dt)=1/(a(x))[c(y)-b(x)];(dy)/(dt)=-a(x)[h(x)-e(t)](1)(其中a(x),b(x),h(x),c(y),e(t)为连续可微函数,x,y∈R,t∈[0,+∞),且a(x)>0)解的有界性及周期解的存在性,并应用该结论讨论了强迫振动方程:x+(f(x)+g(x)x)x+h(x)=e(t)(2)(其中f(x),g(x)为连续可微函数,x∈R,h(x),e(t)同上)解的有界性及周期解的存在性.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.