求解中立型比例延迟泛函微分方程的数值方法

正1引言在本文中,我们主要考虑带有以下边界条件的中立型泛函微分方程(u(t)+a(t)u(pm~t))~(m)=βu(t)+(m-1)∑(k=0)b_k(t)u~(k)(pkt)+f(t),t≥0,(1.1)(m-1)∑(k=0)c_(ik)u~(k)(0)=λ_i,i=0,1,…,m-1,其中a(t)和b_k(t)(k=0,1,…,m-1)是已知的解析函数,β,pk,c_(ik),λ_i为已知的常数且0pk1(k=0,1,…,m).中立型延迟泛函微分方程描述一种特殊的延迟微分方程.这     

变号(k,n-k)共轭边值问题解的存在问题

讨论了下列变号(k,n-k)共轭边值问题(SCBVP)正解的存在问题{(-1)(n-k)u(n)(t)=f(t,u(t)),0t1,u(i)(0)=0,0≤i≤k-1,u(j)=0,0≤j≤n-k-1,其中n≥2,1kn-1.对于0t1,非线性项f允许变号,即本文允许非线性项f取负值并且可以无下界.本文利用不动点指数定理,在无任何单调性假设条件下,得到了边值问题正解的存在性结论.     

奇数阶边值问题正解的存在性与多重性

利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间.     

一类具有非局部扩散的时滞Lotka-Volterra竞争模型的行波解

本文研究一类具有非局部扩散的时滞Lotka-Volterra竞争模型{(δ)/(δ)t u1(x,t)=d1 [(J1*u1)(x,t)-u1(x,t)]+r1u1(x,t)[1 - a1u1(x,t)- b1u1(x,t-Τ1)-c1u2(x,t-Τ2)],(δ)/(δ)tu2(x,t)=d2[(J2*u2)(x,t)-u2(x,t)]+r2u2(x,t)[1 - a2u2(x,t)- b2u2(x,t -Τ3)-c2u1(x,t-Τ4)]行波解的存在性问题.通过利用交叉迭代技巧,我们可以把行波解的存在性转化为寻找一对适当的上下解,这篇文章中的结果推广了已有的一些结果.     

非线性四阶周期边值问题多个正解的存在性

利用不动点和度理论,证明了四阶周期边值问题u(4)(t)-βu″(t)+αu(t)=λf(t,u(t)),0≤t≤1,u(i)(0)=u(i)(1),i=0,1,2,3,至少存在两个正解,其中β>-2π2,0<α<(1/2β+2π2)2,α/π4+β/π2+1>0,f:[0,1]×[0,+∞)→[0,+∞)是连续函数,λ>0是常数.     

VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Ginzburg-Landau equation in a smooth bounded domain Ω  R2, that is, ■tuε = 2Σ/j,k=1 (ajkj■xjkuε)xj + b(x)(1-ε|ε|2)uε/2u, x ∈Ω, and conclude that each vortex bj(t) (j=1, 2,···, N) satisfies dbdjt(t)= -(a1k(bj(t)b)■(xk))a(a (bj(t)), a2k(bj (t))/xk a(bj (t)) a(bj (t)) , where a(x) =(a11a22-a122(1/2)). We prove that all the vortices are pinned together to the critical points of a(x). Furthermore, we prove that these critical points can not be the maximum points.     

SINGULAR (n-1,1) CONJUGATE BOUNDARY VALUE PROBLEMS

In this paper, we study the existence of nonnegative solutions of singular (n - 1,1) conjugate boundary value problemwith boundary value conditions u(k)(0) = 0(0≤k≤n - 2) and u(I) = 0. Where a(t) may have finitely many singularities. Our results essentially generalized paper [1] and other related literature (for example [4]).     

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS

In this article,we study the initial boundary value problem of generalized Pochhammer-Chree equation u_(tt)-u_(xx)-u_(xxt)-u_(xxtt)=f(u) xx,x ∈Ω,t 0,u(x,0) = u0(x),u t(x,0)=u1(x),x ∈Ω,u(0,t) = u(1,t) = 0,t≥0,where Ω=(0,1).First,we obtain the existence of local W k,p solutions.Then,we prove that,if f(s) ∈ΩC k+1(R) is nondecreasing,f(0) = 0 and |f(u)|≤C1|u| u 0 f(s)ds+C2,u 0(x),u 1(x) ∈ΩW k,p(Ω) ∩ W 1,p 0(Ω),k ≥ 1,1 p ≤∞,then for any T 0 the problem admits a unique solution u(x,t) ∈ W 2,∞(0,T;W k,p(Ω) ∩ W 1,p 0(Ω)).Finally,the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed.     

The Aysmptotic Behavior of Solution to a Class of Inhomogeneons Systems of Gas Dynamics

1.IntroductionInthispaper,weresearchsomeclassofinhomogeneonssystemsofgasdynamic:wherevisreciprocalofgasdensity,uisvelocity,6isabsolutetemperatureofgas.p,k,aareconstants.Suppose(t,x)e[0,+~)X[0,fiingeneral,thentheboundaryconditionareu(t,0)~u(t,l)~0,sx(t,0)~gx(t,1)~0,(l.2)theinitialconditionis(v,u,6)(0,x)~(v,,uo,0,)(x),(1.3)andsatisfiessuitableconditionsWheninI相似文献   

GLOBAL SMOOTH SOLUTIONS OF DISSIPATIVE BOUNDARY VALUE PROBLEMS FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS

This paper discusses the following initial-boundary value problems for the first orderquasilinear hyperbolic systems:(u)/(t)+A(u)(u)/(x)=0,(1)u~Ⅱ=F(u~Ⅰ),as x=0,(2)u~Ⅰ=G(u~Ⅱ),as x=L,(3)u=u~0(x),as t=0,(4)where the boundary conditions(2),(3)satisfy F(0)=0,G(0)=0 and the dissipativeconditions,that is,the spectral radii of matrices B_1=(F)/(u~Ⅰ)(0)(G)/(u~Ⅱ)(0)and B_2(G)/(u~Ⅱ)(0)(F)/(u~Ⅰ)(0) are less than unit.Under certain assumptions it is proved that the initial-boundary problem (1)—(4)admits a unique global smooth solution u(x,t)and the C~1-norm丨u(t)丨σ~2of u(x,t)decaysexponentially to zero as t→∞,provided that the C~1-norm丨u~0丨σ~1of the initial data issufficiently small.     

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