具p-Laplacian算子型奇异边值问题多重正解

本文讨论了一类具ｐ－Ｌａｐｌａｃｉａｎ算子型奇异边值问题（φｐ（ｘ＇））＇＋ａ（ｔ）ｆ（ｘ（ｔ））＝０,ｘ（０）－βｘ（０′）＝ ０,ｘ（１）＋ δｘ′（１）＝０多重正解的存在性,其中φｐ（ｘ）＝｜ｘ｜ｐ－２ｘ,ｐ＞１ 通过使用不动点指数定理, 在适当的条件下,建立了这类边值问题存在多重正解的充分条件．这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性．     

非线性三阶微分方程的四点边值问题

用上下解方法研究了三阶非线性微分方程四点边值问题ｕ＝ｆ（ｔ，ｕ，ｕ″），ａ≤ｔ≤ｂ，ｕ（ａ）＝ｕ（ａ０），ｕ′（ａ）－δｕ″（ａ）＝Ａ，ｕ（ｂ）＝ｕ（ｂ０），｛其中ａ＜ａ０≤ｂ０＜ｂ，δ≥０，Ａ是给定常数．证明了ｆ在适当条件下，上述边值问题有解的充要条件是存在一个下解α和上解β使得α（ｔ）≤β（ｔ），ａ≤ｔ≤ｂ．     

关于Banach空间隐式常微分方程的解的存在性

讨论了 Ｂａｎａｃｈ 空间中隐式常微分方程 Ｆ（ｔ,ｘ,ｘ′） ＝ ０, ｘ（ｔ０ ） ＝ ｘ０ , ｘ′（ｔ０） ＝ ｙ０ 的解的存在性,其中, Ｆ 的定义域可含无穷远点     

具有强非线性源非牛顿多方渗流方程解的极限性质

研 究如下第一边值 问题ｕ ｔ ＝ ｄｉｖ（｜ Ｄｕ ｍ ｜ｐ － ２ Ｄｕｍ ） ＋ ｆ （ｘ ,ｕ）ｕ （ｘ ,ｔ） ＝ ０ｕ （ｘ ,０） ＝ ｕ０  ０ 　 　　　（ｘ ,ｔ） ∈ Ｑ Ｔ ＝ Ω× （０, Ｔ）（ｘ ,ｔ） ∈ Ω× （０, Ｔ）ｘ ∈ Ω解的极限性质 （ｔ → ∞）,推 广了文献［１ ～ ７］ 的结果     

关于Fujita型反应扩散方程组的Cauchy问题

本文研究Ｆｕｊｉｔａ型反应扩散方程组ｕｔ－Δｕ＝α１｜ｕ｜ｑ１－１ｕ＋β１｜ｖ｜ｐ１－１ｖ，（ｘ∈ＲＮ，ｔ＞０），ｖｔ－Δｖ＝α２｜ｕ｜ｑ２－１ｕ＋β２｜ｖ｜ｐ２－１ｖ，ｕ（ｘ，０）＝ｕ０（ｘ）０，ｖ（ｘ，０）＝ｖ０（ｘ）０，（ｘ∈ＲＮ）Ｌｐ解的整体存在性和有限时间Ｂｌｏｗ ｕｐ问题．这里ｑｉ＞１，ｐｉ＞１（ｉ＝１，２），α１０，α２＞０，β１＞０，β２０，１ｐ＋∞．     

一类非自治迭代泛函微分方程

本文研究了一类非自治迭代泛函微分方程ｘ′（ｔ）＝（ｘ２（ｔ）－ｔ２）ｆ（ｘ（ｘ（ｔ）））（其中ｆ∈Ｃ（Ｒ，Ｒ），单调递增，ｚｆ（ｚ）＞０，ｚ≠０）满足初始条件ｘ（σ）＝σ＞０，或满足初始条件ｘ（σ）＝－σ＜０的解的性态、解的存在性及延拓问题．     

对合重特征边值问题的奇性反射

设ΩＲ（ｎ＋１），其边界　Ω在ｘ０∈　Ω附近局部为｛ｔ＝０｝，且对ｍ阶偏微分算子Ｐ（ｘ，ｔ，Ｄｘ，Ｄｔ）是非特征的．令σｍ（Ｐ）（ｘ，ｔ，ζ，Ｔ）＝０关于Ｔ有ｍ个实根（包括重根）λｊ（ｘ，ｔ，ζ），（ｊ＝１，．．．，ｍ），且它们是对合组．在Ｐ（ｘ，ｔ，Ｄｘ，Ｄｔ）满足Ｌｅｖｉ条件下，则其Ｄｉｒｉｃｈｌｅｔ边值问题的解ｕ的Ｃ∞奇性在边界的反射锥族中是不变的．     

高校应用数学学报第14卷(1999年)B辑(英文版)第1期目次和提要

具有扰动项的泛函微分方程周期边值问题刘辉昭（河北工业大学应用数学系）蒋达清（东北师范大学数学系）利用重合度证明了具有扰动项的混合型泛函微分方程周期边值问题ｘ（ｔ）＝ｂ（ｔ,ｘｔ）＋Ｇ（ｔ,ｘｔ）,０≤ｔ≤Ｔ,ｘ（０）＝ｘ（Ｔ）．｛解的存在性,这里ｘ（...     

具有分段常数变元的时滞微分方程解的振动性(英文)

我们获得了带有分段常数变元的时滞微分方程ｘ′（ｔ）＋ａ（ｔ）ｘ（ｔ）＋∑ｍｉ＝１ｂｉ（ｔ）ｘ（［ｔ－ｉ］）＝０，ｔ≥０所有解振动的新的充分条件，这里［·］定义为最大整数函数．我们的结果改进了文献中的某些已知结果．     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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.     

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 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.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in