POSITIVE SOLUTIONS OF TWO-POINT BOUNDARY VALUE PROBLEMS OF DIFFERENTIO-INTEGRAL EQUATIONS

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅｆｏｌｏｗｉｎｇｓｅｃｏｎｄｏｒｄｅｒｎｏｎｌｉｎｅａｒｄｉｆｅｒｅｎｔｉｏ－ｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎ...     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｉｎｉｔｅｖｏｌｕｍｅｅｌｅｍｅｎｔｍｅｔｈｏｄｏｒＦＶＥＭｕｓｅｓａｖｏｌｕｍｅｉｎｔｅｇｒａｌｆｏｒｍｕｌａｔｉｏｎｏｆｔｈｅｄｉｆ ｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｉｔｈａｆｉｎｉｔｅｐａｒｔｉｔｉｏｎｉｎｇｓｅｔｏｆｖｏｌｕｍｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｅｑｕａｔｉｏｎ ,ｔｈｅｎｒｅ ｓｔｒｉｃｔｓｔｈｅａｄｍｉｓｓｉｂｌｅｆｕｎｃｔｉｏｎｓｔｏａｌｉｎｅａｒｆｉｎｉｔｅｅｌｅｍｅｎｔｓｐａｃｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｓｏｌｕｔｉｏｎ ([1 -4 ] ) .…     

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅ１９７０，ｔｈｅｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｆｕｎｃｔｉｏｎａｌｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｈａｖｅｂｅｎｄｅｒｉｖａｔｉｖｅｄｆｒｏｍｍａｎｙｆｉｅｌｄｓ，ｓｕｃｈａｓｂｉｏｌｏｇｙ...     

POSITIVE SOLUTIONS OF SINGULAR SUPERLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｏｆｓｅｃｏｎｄｏｒｄｅｒｏｒｄｉｎａｒｙｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｘ″＋ｐ（ｔ）ｆ（ｘ）＝０，ｔ∈（０，１），（１）ａｘ（０）－ｂｘ′（０）＝０...     

REGULARITY OF THE FREE BOUNDARY IN ELECTROCHEMICAL MACHINING PROBLEM

ＲＥＧＵＬＡＲＩＴＹＯＦＴＨＥＦＲＥＥＢＯＵＮＤＡＲＹＩＮＥＬＥＣＴＲＯＣＨＥＭＩＣＡＬＭＡＣＨＩＮＩＮＧＰＲＯＢＬＥＭＹｕａｎＧｕａｎｇｗｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ...     

A CHARACTERIZATION OF THE EMBEDDABILITY OF GRAPHS ON THE SURFACE OF GIVEN GENUS

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｙｍｂｏｌｓａｎｄｔｈｅｔｅｃｈｎｉｃａｌｔｅｒｍｓｎｏｔｅｘｐｌａｉｎｅｄｉｎｔｈｉｓｐａｐｅｒｃａｎｂｅｆｏｕｎｄｉｎ[1]ａｎｄ[3].ＡｇｒａｐｈｉｓｏｆｔｅｎｄｅｎｏｔｅｄｂｙＧ=(Ｖ,Ｅ),υ=｜Ｖ｜ａｎｄε=｜Ｅ｜ａｒｅｃａｌｌｅｄｉｔｓｏｒｄｅｒａｎｄｓｉｚｅｒｅｓｐｅｃｔｉｖｅｌｙ.ＩｔｈａｓｂｅｅｎｓｈｏｗｎｂｙＲ.Ｄｕｋｅ[4]ｔｈａｔｉｆａｃｏｎｎｅｃｔｅｄｇｒａｐｈＧｈａｓｅｍｂｅｄｄｉｎｇｓ(ｏｒ2-ｃｅｌｌｅｍｂｅｄｄｉｎｇｓｉｎＤｕｋｅ’ｓｔｅｒｍｉ…     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

ON A CLASS OF SIMPLE TABLE ALGEBRAS

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＺ.ＡｒａｄａｎｄＨ.Ｂｌａｕｉｎｔｒｏｄｕｃｅｄｉｎ[1]ｔｈｅｃｏｎｃｅｐｔｏｆｔａｂｌｅａｌｇｅｂｒａｓａｎｄｕｓｅｄｔｈｉｓｔｏｄｉｓｃｕｓｓｔｈｅｃｈａｒａｃｔｅｒａｌｇｅｂｒａａｎｄｔｈｅｃｅｎｔｒａｌｃｌａｓｓａｌｇｅｂｒａｏｆａｆｉｎｉｔｅｇｒｏｕｐｉｎａｕｎｉｆｏｒｍｗａｙ.ＴｈｉｓｉｄｅａｇｏｅｓｂａｃｋｔｏＩ.Ｓｃｈｕｒ.ＡｌｉｔｔｌｅｅｘｔｅｎｄｅｄｎｏｔｉｏｎｏｆＣ-ａｌｇｅｂｒａｆｏｒｅｓｈａｄｏｗｅｄｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｃｏｍｍｕｔａ…     

NOTE ON A BOUNDARY VALUE PSOBLEM OF POISSON''''S EQUATION

ＮＯＴＥＯＮＡＢＯＵＮＤＡＲＹＶＡＬＵＥＰＳＯＢＬＥＭＯＦＰＯＩＳＳＯＮ＇ＳＥＱＵＡＴＩＯＮ￥ＦＥＮＧＣＨＡＯＫＥＮＧ；ＨＳＵＬＩＺＨＩ；ＡＮＤＹＵＨＯＮＧＱＵＡＮＡｂｓｔｒａｃｔ：ＴｈｉｓｎｏｔｅｓｈｏｗｓｔｈａｔｆｏｒａＢＶＰｏｆＰｏｉｓｓｏｎ＇...     

HARMONIC MAPS AND FUNDAMENTAL GROUPS OF NONPOSITIVELY CURVEDRIEMANNIAN MANIFOLDS

Ｔｈｅｔｈｅｏｒｙｏｆｈａｒｍｏｎｉｃｍａｐｓｉｎｔｏａｃｏｍｐａｃｔｎｏｎｐｏｓｉｔｉｖｅｌｙｃｕｒｖｅｄｔａｒｇｅｔｉｓｗｅｌｌ-ｄｅｖｅｌｏｐｅｄ.ＴｈｅｅｘｉｓｔｅｎｃｅｏｆｓｕｃｈａｈａｒｍｏｎｉｃｍａｐｐｉｎｇｉｎａｎｙｇｉｖｅｎｈｏｍｏｔｏｐｙｃｌａｓｓｉｓｅｓｔａｂｌｉｓｈｅｄｂｙＥｅｌｌｓａｎｄＳａｍｐｓｏｎ[1]ｉｎ1964,ａｎｄｌａｔｅｒ,ｉｎ1967,Ｈａｒｔｍａｎ[2]ｇａｖｅａｐｒｏｏｆｏｆｔｈｅｕｎｉｑｕｅｎｅｓｓ.Ｔｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏａｎａｐｐｌｉｃａｔｉｏｎｏ…     

UNSTEADY BOUNDARY LAYER FLOW OF FRACTIONAL OLDROYD-B VISCOELASTIC FLUID PAST A MOVING PLATE IN A POROUS MEDIUM

This paper considers the unsteady boundary layer flow over a moving flat plate embedded in a porous medium with fractional Oldroyd-B viscoelastic fluid. The governing equations with mixed time-space fractional derivatives are solved numerically by using the finite difference method combined with an L1-algorithm. The effect of various physical parameters on the velocity and average skin friction are discussed and graphically illustrated in detail.Results show that the porosity € and fractional derivative α enhance the flow of Oldroyd-B viscoelastic fluid within porous medium, but fractional derivative βweakens the flow. Moreover, it is found that the average skin friction coefficient rises with the increase of fractional derivative β.     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...     

THE GLOBAL SOLUTION OF INITIALBOUNDARY VALUE PROBLEM OF HIGHER-ORDER MULTIDIMENSIONAL EQUATION OF CHANGING TYPE

In practical problems there appears the higher-order equations of changing type. But,there is only a few of papers, which studied the problems for this kind of equations. In this paper a kind of the higher-order m     

次线性条件下奇异三阶微分方程周期边值问题解的全局结构

讨论三阶微分方程周期边值问题解的全局结构,其中ρ∈(0,1/3~(1/2))为常数,λ∈R~+=[0,+∞)为参数,f在t=0,t=2π和u=0处有奇异性,关于u处满足次线性增长条件。     

n阶非线性常微分方程组边值问题的正解

运用不动点指数理论,研究以下$n$阶非线性常微分方程组边值问题正解的存在性和多重正解的存在性\[\left\{\ay\begin{array}{l}-u^{(n)}=f_1(x,u,v),\q-v^{(n)}=f_2(x,u,v),\\[2mm]u^{(i)}(0)=u^{(p)}(1)= v^{(i)}(0)=v^{(p)}(1)=0.\end{array}\right. \] 这里$n\geq 2$, $i = 0,1,2,\cdots,n-2$, $p \in \{1,2,\cdots,n-1\}$, $f_i\in C([0,1]\times\mathbb R^+\times\mathbb R^+,\mathbb R^+)~(i=1,2)$. 用凹函数刻画非线性项$f_1,f_2$的耦合行为, 因而非线性项 $f_i(i=1,2)$ 既可以都是超线性的, 也可以都是次线性的,还可以是混合非线性的(即其中一个是超线性的, 另一个是次线性的).     

二阶两点边值问题单调正解的存在性

考察了形如{x″(t)+f(t,x(t))=0,0≤t≤1,x(0)=ξx(1),x′(1)=ηx′(0)的二阶非线性微分方程两点边值问题,这里ξ,η∈(0,1)∪(1,∞)为给定的常数,f:[0,1]×[0,∞)→[0,∞)连续。在某些适当的增长性条件下,应用Avery-Anderson-Krueger不动点定理证明了单调正解的存在性。     

THE GLOBAL SMOOTH SOLUTIONS OF SECOND ORDER QUASILINEAR HYPERBOLIC EQUATIONS WITH DISSIPATIVE BOUNDARY CONDITIONS

The paper deals with the following boundary problem of the second order quasilinear hyperbolic equation with a dissipative boundary condition on a part of the boundary:u_(tt)-sum from i,j=1 to n a_(ij)(Du)u_(x_ix_j)=0, in (0, ∞)×Ω,u|Γ_0=0,sum from i,j=1 to n, a_(ij)(Du)n_ju_x_i+b(Du)u_t|Γ_1=0,u|t=0=φ(x), u_t|t=0=ψ(x), in Ω, where Ω=Γ_0∪Γ_1, b(Du)≥b_0>0. Under some assumptions on the equation and domain, the author proves that there exists a global smooth solution for above problem with small data.     

N维多重非齐次调和方程及其边界积分方程

对n维多重非齐次调和方程△~((k))u=f(x),x∈R~n,给出了基本解的递推公式以及多重调和函数的积分关系式.在非齐次项f(x)为m次调和的情形下将域上的积分转化为沿边界的积分,进而应用直接法给出了基本边界积分方程.对f(x)为一般光滑函数的情形,给出了用泰勒多项式逼近时相应的误差估计并证明了含误差项的积分是收敛的.     

BOUNDARY LAYER ESTIMATION OF THE QUASILINEAR STOKES EQUATIONS

1IntroductionConsidertheequationwhereaisaconstantin(0,1).ThesolutionisclearlyWenowomittheviscositytermandaboundaryconditionof(1.1)asfollows:Thesolutionof(1.2)isForesmallandx>E,thetwosolutionsareclosetogether.Theregionwheretheyaredrasticallydifferentisconfinedtotheinterval[0,E],whichisthesthcalledboundarylayer.Notesthatase~0,theboundarylayershrinkstozero,hiltthemaximumdifferencebetweenIReceivedMar.9,1995;revisedSep.18,1996.ThisworkissupportedbyFoundationoflhstituteofMathematics,Acadedasin…     

DIRICHLET FROBLEMS FOR MONGE-AMPERE EQUATION DEGENERATE ON BOUNDARY

The existence of $\[{C^\infty }\]$ solutions to Dirichlet problem for Monga-Ampere equation degenerate on boundary