关于一类拟线性椭圆型方程带有间断边值的Dirichlet问题的注记

<正> 任朝佐在文[1]中讨论了拟线性椭圆型方程Δu(x,y)+f(x,y,u,((?)u)/((?)x),((?)u)/((?)y))=0带有间断边值的 Dirichlet 问题解的存在性、唯一性及间断点附近的性质.本文将这些加以推广,讨论更一般的拟线性椭圆型方程Lu≡a(x,y)((?)~2u)/((?)x~2)+2b(x,y)((?)~2u)/((?)x(?)y)+c(x,y)((?)~2u)/((?)y~2)+f(x,y,u,((?)u)/((?)x),((?)u)/((?)y))=0 (1)的类似问颢,得到相应的结果,而且区域也取消了[1]中的凸性的限制.     

非经典反应扩散方程在R~3中全局吸引子的存在性

该文证明了带有临界非线性项的非经典反应扩散方程{vt-Δvt-Δu+f(x1,u)=g(x),(x,t)∈R3×R+ u(s,t)|t=0=v0, x∈R3}在H~1(R~3)上的全局吸引子的存在性,推广和改进了文献[15]的结果.     

带平均曲率算子的离散混合边值问题凸解的存在性北大核心CSCD

运用锥上的不动点定理讨论了Minkowski空间平均曲率算子的离散混合边值问题Δ[Φ(Δv(t-1))]=f(t,-v(t)),t∈[2,T-1]z,Δv(1)=0,v(T)=0非平凡凸解的存在性,其中Φ(s)=s/√1-x^(2),s∈(-1,1),[2,T-1]z:={2,3,……T-2,T-1},T≥4是正整数,非线性项f(t,u)非负连续,在u=1处允许具有奇异性.     

非线性梁振动方程的周期解

一、引言考虑下述问题Ku″ A~2u M(‖A~1/2u‖~2)Au Au′=f(x,t),t>0,x∈Ω,(1.1)u|_t=0~=u_0(x),x∈Ω,(1.2)Ku′|_(t=0)=u_1(x),x∈Ω,(1.3)u=0,x∈(?)Ω,t≥0 (1.4)的ω-周期解的存在性.其中 Ω(?)R~n 为一有界光滑区域,u′=((?)u)/((?)t),u_″=((?)u)/((?)t)~2,K 为有界线性对称算子且满足(Ku,u)≥0,M∈C~1[0,∞),M(ξ)≥-β,ξ≥0.此模型最初由Woinowsky 和 Krieger 提出,方程形式为     

一类带弱奇异核非线性偏积分微分方程的全离散有限元

1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献   

一类二阶四点边值问题正解的存在性

讨论二阶四点微分方程组边值问题u″+p(t)f(t,u(t),v(t))=0,0 t 1,v″+q(t)g(t,u(t),v(t))=0,0 t 1,u(0)=a1x(ξ1),u(1)=b1x(η1)v(0)=a2x(ξ2),v(1)=b2x(η2)如果函数f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)是连续的,并赋予f、g一定的增长条件,利用Leggett-Williama不动点定理,证明了上述边值问题至少存在三对正解.     

一类带临界指数增长的椭圆型方程组两个正解的存在性

该文主要讨论带临界指数的椭圆型方程组{-Δu + a(x)u =2α/α+βuα-1vβ + f(x),x ∈Ω,-Δv+b(x)v=2β/α+βuαvβ-1+ g(x),x ∈ Ω,(*)u ＞ 0,v ＞ 0,x ∈Ω,u=v=0,x ∈(a)Ω解的存在性,其中Ω是RN中一个光滑有界区域,N=3,4,a≥2,β≥2...     

FINITE ELEMENT ANALYSIS OF A LOCAL EXPONENTIALLY FITTED SCHEME FOR TIME-DEPENDENTCONVECTION-DIFFUSION PROBLEMS

1.IntroductionConsiderthetime-dependentconvection-diffusionproblemat--Euzx a(x,t)u. b(x,t)u~f(x,t),(x,t)E[0,1]x[0,T](1.1)u(0,t)=u(1,t)~0,tE[0,T].(1.2)u(x,0)=u000,xE[0,1],(1.3)a(x,t)2or>0,(1.4)b(x,t)--a.(x,t)/220>0,(1.5)where0SE<<1'(1.1)-(1.5)canbereg...     

AN EFFECT ITERATION ALGORITHM FOR NUMERICAL SOLUTION OF DISCRETE HAMILTON-JACOBIBELLMAN EQUATIONS

§1Introduction ConsidertheHamilton-Jacobi-Bellmanequation max1≤v≤m[A(v)u(x)-f(v)(x)]=0,x∈Ω(1.1)withtheboundarycondition u(x)=0,x∈Ω(1.2)whereΩisabounded,smoothdomaininEuclideanspaceRd,d∈N;f(v)(x)aregiven functionsfromC2(Ω);A(v)aresecond-orderuniformlyellipticoperatorsoftheform A(v)=-d i,j=1a(v)ij2xixj+di=1b(v)ixi+c(v).(1.3)Intheaboveexpression(1.3)therearecoefficientsa(v)ij,b(v)i,c(v)∈C2(Ω)satisfying,forall1≤v≤m,a(v)ij(x)=a(v)ji(x),1≤i,j≤d,c(v)≥c0≥0,x∈Ω,a…     

二阶多点边值问题多个正解存在性

利用Leggett-Williams不动点定理,并赋予f,g一定的增长条件,证明了二阶多点微分方程组边值问题u″+f(t,u,v)=0,v″+g(t,u,v)=0,0 t 1,u(0)=v(0)=0,u(1)-∑n-2i=1kiu(ξi)=0,v(1)-∑m-2i=1liv(ηi)=0,至少存在三对正解,其中f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)是连续的.     

一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

一类pnm阶群的构造

本文研究了一类特殊的pnm阶有限群的构造.利用求解数论同余方程的方法和群的扩张理论,得到了具有m阶循环正规子群,其补子群为循环群的Pnm阶有限群的构造及相关的计数定理.     

COMPARISON OF PRODUCTS OF THE VARIETIES OF LIE ALGEBRAS

Abstract

In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle.     

ADDITIVE FAMILIES OF INVARIANTS OF FORMS OF DEGREE d

Abstract

Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I _n, is a GL _n,(F)- invariant of forms of degree d in x₁, …, x _n, over F. We call {I _n} an additive family of invariants if I _p+q (f ⊥ g) = I _p(f).I _q(g) whenever f; g are forms of degree d over F in x _l, …, x _p; …, x _q respectively, and where (f ⊥ g)(x _l, …, x _p+q) = f(x ₁, …, x _p,) + g (x _p+1, …, x _p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review.     

ESTIMATES OF N-FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.     

小康判别函数的建立与分析

近几年，国内在研究小康水平的定量指标分析中，应用较多的有综合评分法、层次分析法和模糊识别法。这几种方法比单项指标更全面、灵活，但在权数的确定上都难以克服人为因素的影响。当指标之间存在两个或两个以上的高度相关时，对问题的研究总存在一定的局限性。为了科学地研究小康问题，本文基于判别分析，建立城市小康的判别系数，来综合评价出我国城市小康水平的定量标准。     

有限Abel群上子集等价类的计数

设G为一有限Abel群，|G|=v,D1,D2是G的两个子集，如果存在t∈Zv,(t,v)=1,s∈G使D1＝tD2 s，则称D1与D2是等价的。文中给出了G的k-子集等价类的计数公式，同时也给出了G的的所有子集等价类的计数公式。