有序Banach空间常微分方程的正周期解

依据凝聚锥映射的一个krasnoselskii型不动点定理，在有序Banach空间中获得了二阶常微分方程．-u^n(t) Mu(t)＝f(t,u(t))正ω—周期解的存在性结果。     

关于Heisenberg群上次Laplace算子的唯一延拓性

在Heisenberg群Hn中对微分不等式|△Hnu|≤C/d(z,t)2ψ|u|的非负解证明了某个唯一延拓性结果.     

完全非线性扰动方程的线性化原理

本文讨论方程u_i=a(t,εu,ε▽u,ε▽u)·▽u f(t,x,u,▽u)带第一初边值条件的解的存在性,其中a(t,0,0,0)>0,当|ξ|相似文献   

某类沿曲线的振荡积分

对R2上沿曲线(t,γ(t))的振荡积分算子τα,βf(x, y) = ∫R f(x - t, y - γ(t))e-i|t|-βt-1|t|-αdt进行了研究,其中γ(t)=|t|κ或γ(t)=sgn(t)|t|κ,α,β,κ为使得算子τα,β有定义的任意实数.假设αβ＞0,|β|＞3|α|以及β≠1,得到τα,β在Lp(R2)上有界,当且仅当κ≠β,其中p ∈ (2β/(2β-3α),2β/3α).     

完备三分图K(A、B、C)有同构因子的某些充分条件

如果图G(V,E)可以分解成t个彼此同构的边不重子图G_1,…,G_t的并,则称G有t个同构因子。或者说t可分G,记为t|G。若G有q条边,t|G的一个明显的必要条件是t|q,并称之为t|G的可分性条件。Harary Robinson和Worrnald证明了对于完备三分图K(m,n,s)当t=2、4时t|mn ms 是t|K(m,n,s)的充分条件,且猜测t为偶数时t|mn ms ns是t|K     

Kirchhoff吊桥方程解的长时间行为

利用Faedo-Galerkin方法获得了问题弱解和强解的存在唯一性及解对初值的连续依赖性,并运用有界吸收集的存在性刻画了与问题相关的动力系统(X0,S(t))的耗散性.当非线性阻尼项|ut|put中的p＞0时,证明了动力系统(X0,S(t))的渐近光滑性;而当p=0时,得到了动力系统(X0,S(t))的拟稳定性.基于...     

测度链上非线性微分方程的三正解

运用文[1]中的Leggett—Williams不动点定理，我们给出了测度链上的非线性微分方程-x^△△(t)=f(t,x(σ(t))),t∈[a,b,]关于两点边值条件ax(a)-βx^△(a)=0，γx(σ(b)) δx^△(σ(b))=0三正解存在性准则。     

Zygmund函数在闭区间上最大值的估计

对任意实数集 R上的 Zygmund函数 f(x) ,满足条件 :|f(x+t) - 2 f(x) +f(x- t) | ‖ f‖z|t|,x,t∈ R ,且 f(0 ) =f (1 ) =0 ,本文证明maxx∈ [0 ,1 ] |f(x) | 13‖ f‖z.     

ON HILBERT BOUNDARY VALUE PROBLEMS WITH RADICAL

The Hilbert boundary value problemRe{λ(t) P√ψ (t)} = c(t), t ∈ Lof normal type with Holder continuous coefficients is discussed, where Lis the unit circle |t| = 1,p ≥ 2 is any definite integer, Ψ (t) is the boundary value of the unknown function Ψ (z) holomorphic in |z| ＜ 1 with single-valued continuous P√ψ (t)} on L.     

双重退化抛物型方程整体解的存在性和L~∞估计

文考虑双重退化抛物型方程ut=div(|u|r|u|m--2u)+A(u)带有零边界条件的初边值问题的整体解存在性,唯一性和解在t=0,∞处的L∞模估计.证明了当u0∈Lq(Ω)时,整体解u(t)满足估计‖u(t)‖∞≤C(1+t-λβ)(1+t)-β/M,‖(u(t)|r/(m-1)u(t))‖m≤C(1+t-μ)(1+t)-σ,t＞0,这里λ,μ,σ,M,β为依赖于m,q,N和r的适当正常数.     

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

正~~     

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].