一阶椭圆型方程组的黎曼——哈斯曼边值问题(Ⅱ)

设L是平面E上一条简单的光滑闭曲线,它把E分成含有坐标原点的内部有界区域D~+和包含无穷远点的外部无界区域D~-,L的正方向是使区域D~+位于其左边的方向。对于一阶复式的椭圆型方程组 (1)维库阿建立了所谓广义解析函数的理论,其中假设方程(1)的系数A(z),B(z)∈L_(p,2)(E),p>2。不失一般性,可设A(z)=0,这种情形的方程(1)称为标准形方程。     

广义解析函数带位移的一个四元素边值问题

一、问题的提法假设 D~ 是由一组简单、封闭、曲线 L_0。L_1,……,L_m 所围成的平面有界多连通区域,其中 L_0包含所有其它的 L_j(j=1,……,m)在其内部。记 L=()L_j,用 D~-表示D~ UL 到全平面的余集。显然有 D~-=()DJ,其中 D_0~-为 L_0外部的无界区域,D_j~-(j=1,…     

关于幂型非线性边值问题

§1 问题的叙述考虑在沿区间[0,1]切开的复平面上,求一个全纯函数Φ(z)=u+iv,使其满足条件(1) [Φ~+(t)]~a+[Φ~+(t)]~a=f(t),f∈(0,1),0相似文献   

THE COMPOUND BOUNDARY VALUE PROBLEM FOR A CLASS OF NONLINEAR PSEUDOPARABOLIC SYSTEMS

Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves _0, _1…, _N and _1… _N are in the interior of domain circumscribed byC_μ~1(0 <μ< 1). In addition, assume that there are n mutually exclusive contour γ_,j=1,…,n,in interi-or of D,γ=γ_i; ∈C_μ~1. Denote D_j is the bounded domain circumscribed by γ_j,j=1,…,n, D~-=D_1+…+D.,D~+=D-D~-,D_t~ =D~ ×E, E=[0,T] (T>0), z=0∈D~+.We consider the following pseudoparabolic complex equation on D_t~ : / t[W_Z- Q_1(z)W_z- Q_2(z) _ - A_1(z)W - A_2(Z) ]= H(t,z,W,W-_2,W_2), (z,t) ∈D_t~ , (1)     

关于幂型非线性边值问题

§1 问题的叙述考虑在沿区间[0,1]切开的缸平面上,求一个全纯函数φ(z)=u+iv,使其满足条件 (1) [φ~+(t)]~a+[φ~-(t)]~a=f(t),t ∈(0,1),0相似文献   

ON THE COMPOUND BOUNDARY PROBLEM FOR DOUBLY-PERIOD WITH SHIFT

In this paper, we will discuss a kind of the compound boundary problem for doubly-period-Haseman-Carleman boundary Problem Rm with doubly-period (simply called H-C Problem Rm) :To find a doubly-periodic function φ(z) analytic in S~+ and S~- except z=0 (including the union of z= 0 with periods 2ω_1, 2ω_2) and φ(z) may have m order of singularity at z= 0, which satisfies the follow-ing boundary condition:where a(t) is sense-preserving homeomorphic mapping on L_1 and α′(t)≠0,α′(t)∈H(L_1), α(t+2n_1ω_1+     

关于LD＊设计的一个递归定理

本文给出了三D~*设计的一个递归构造,证明了如下结论:X为n元集,I_v=[0,v],且存在LD~*[X]={L_1~1,L_1~2,L_x;x∈X}和LD~*[I_v]={L_2~1,L_2~2,L_i;i∈I_v},若满足条件:(i_0,i_1,i_2,i_3)∈L_2~1当且仅当(i_1,i_0,i_2,i_3)∈L_2~2,则存在LD~*[X×I_v]。     

THE RIEMANN TYPE BOUNDARY VALUE PROBLEM FOR THE ELLIPITIC SYSTEMS WITH THE BOUNDARY CONDITION INCLUDING HIGHER OREDER DERIVATIVES

Let D~+ be simply connected bounded domain with the boundary ∈C_(n~n);(02. The so-called Riemann type boundary problem of complex equation (1) is to find a piecewise regularsolution w (z) in D, whose boundary value ~kw (t)/ ~k(k=0,1,…,n) continuous on and satisfyingthe boundary condition     

THE DIRECT METHOD OF FINDING SOLUTION FOR HIGHER SINGULAR INTEGRAL EQUATION

As for higher singularity integral equation:its solvability conditions have been investigated in reference [1]. In reference [2], the direct solutionmethod has been discussed. In this paper, we will discuss a kind of method of directly finding solution.As n=2, the equation (1) equivalent to the following;here L is a simple closed curve; D~+, D~-, are the inner-field and outer-field respectively, which are sur-rounded by curve L, we need (t)∈ H_1 (L).Assume that N_x(z,ζ) =(k_v(z,ζ)-k_v(z,ζ))/a_2(z)+b_2(z) is meromorphic on × ,v = 1,2,3. Furthermore it     

星形函数中的特殊子类

1.用A表示在|z|<1内解析且f(0)=f(0)-1=0的函数全体,对α>—1令 D~αf(z)=f(z)* (z/(1—z)~(α+1)),(|z|<1)。则有D~αf(z)∈A 其中记号“*”表示Hadamard乘积。特别当α=n是正整数时,有     

涉及导函数与分担亚纯函数的正规定则

针对涉及导函数与分担亚纯函数的正规定则,得到了如下结果:设Ω是区域D内的亚纯函数族,a(z)(≠0)是亚纯函数。若对于任意μ(z)∈Ω满足如下条件:(1)μ(z)≠0;(2)对μ(z)和a(z)的任意公共极点,其在μ(z)中的重级大于或等于在a(z)中的重级;(3)对任意函数对{μ(z),ν(z)}?Ω,μ~((m))(z)和ν~((m))(z)分担a(z),则Ω在D内正规。同时,给出了2个例子来说明条件(1)和(2)的必要性。     

关于P叶函数的一个子类

本文利用Rusheweyh导数引进函数类T(α+p—1,β)={f(z)|f(z)∈A(p),Re(D~(α+p)f)/(D~(α+p-1)f>β}。当0≤β≤1/2时,证明了T(α+p,β)(?)T(α+p-1,β)。还讨论了由积分算子定义的函数F(z)=(p+c)·z~(-(?))integral from n=0 to z t~((?)-1)f(t)dt,(|z|<1)的映射性质。推广了某些文献中的一些结果。     

ЛЯПУНОВ稳定性理論与含小参数的微分方程

§1.定理的陈述 1.考虑含小参数的微分方程组其中x与f为n维向量,z与F为m维向量,μ>0是小参数.当μ=0时(1.1)变成设D_0~*为(t,x)空间内一区域,在D_0~*上z=φ(t,x)是F(t,x,z,0)=0的一个根.令R~*={(t,x,z)|z=φ(t,x),(t,x)∈D_0~*}. 我们称为(1.1)的退化方程组. 设D_0~*是(t,x,z)空间内含集合R~*的某域,δ>0为某定数.我们假定:φ(t:x)在     

L_2內函数的导数及其Fourier变式

本文定理5和定理6补充了[1]中相应定理的漏洞,定理1和定理2的主要意义在于证明当f(x)∈L_2(-∞,+∞),xf(x)∈L_2(-∞,+∞)时的局部绝对连续变式的存在性([1]中相类似的定理证明有误):定理3指出当f(x)∈L_2(-∞,+∞),T[f]=φ(t),φ(t)∈L_1(-∞,+∞)时普遍的反演公式几乎处处成立;定理4将L_1中的相应定理推广到L_2。     

非零单叶函数的一个极值问题

1.设S_0={f|f在单位圆域△内单叶解析,无零点.f(0)=1},显然,若f(z)∈S_0,则,f~*(z)=f(z)∈S_0,f_(?)(z)=f(e~(?)z)∈S_0由[1]知S_0中的极值问题m(r)=min (?) Ref(r)在S_0中能够达到.1980年,Duren和Schober证明: 若0相似文献   

RIEMANN-HILBERT PROBLEMS OF ELLIPTIC SYSTEM OF FIRST ORDER IN FRACTIONAL SPACES

Let D be a (N+1)-connected domain with the boundary = _j∈C_μ~1(0<μ<1) , where _j(j=0,1,…, N) are simple closed curves and _j(j=1,…,N) are situated inside _0={|z| =1}, and z=0∈D, we consider the complex elliptic equation of first orderwhereProblem A: Find a continuously differentiable solution W(z) on D, which satisfies the boundary con-ditionwhere λ(t) , f (t)∈B_(p~1/P),1( )→C( ), and these satisfy confition C;     

一类解析函数的Fekete-Szeg ? 不等式

利用微分从属构造了解析函数类H(α,A,B)={f(z)∈H:(1-α)f(z)/z+αf'(z)(1+Az)/(1+Bz),z∈U},其中0≤α≤1,-1≤BA≤1,z∈U.利用施瓦兹函数的Fekete-Szeg ?不等式,得到了该函数类上的a_2及a_3-μa_2~2(μ∈C)的精确估计:a_3-μa_2~2≤(A-B)/(1+2α)max {1|,B+(μ(1+2α)(A-B))/((1+α)~2)},并给出了相应的极值函数,其结果推广了已有的结论.     

NONLINEAR GENERALIZED HASEMAN BOUNDARY VALUE PROBLEMS FOR FIRST ORDER QUASILINEAR ELLIPTIC SYSTEMS IN THE PLANE

1 Problems and ConditionsA class of the lst order quasilinear elliptic systems in the plane, on the basis of Douglis algebra, can bewritten in the simple form Dw=F(z. w) , here D = / x+ / y+e(a / x+ / y) be the Douglis opearator[1], F be a hypercomplex function.Let be a simple and smooth closed curve in the complex plane C,D~+ be the simple connected domainbounded by and D~-=C- (D~+ ∪ ). Out problem is to find piecewise regular solutions w(z) for Dw=F(z,w) with jump curve in the whole plane that have fixed integer order at infinity and satisfy the condi-tion on ; w~+ (τ) = G_1(τ)w~- (a(τ)) + G_2(τ)w~+ (β(τ)) +g(τ,w+ (τ),w~- (τ)), which be calledthe nonlinear generalized Haseman boundary value problems. By suitable transformations the problem can     

THE NOETHER THEORY DIRICHLET PROBLEM OF THE SINGULAR INTEGRAL-DIFFERENTIAL EQUATION ON A BOUNDED DOMAIN

In this paper we discusse the Dirichlet problem of the singular integral-differential equation on abounded region in the complex planewhere is a completely continuous operator on L,(G)·a_i(z), b_i(z), c_i(z), d_i(z)∈W_p~I(G), i=1,2,3, p>2,w(z)∈G_α( )∩W_p~1(G), a=(P-2)/p·The main results are as following:The problem     

关于黎曼—希尔伯特边值问题的奇异情形

所谓解析函数于多(N 1)连通区域G上的黎曼一希尔伯特边值问题,即求在(?)上连续、在G内解析的函数Φ(z),使其适合边界条件: (1.1) Re[(?)Φ(Z)]=γ(Z),Z_∈Γ,这里Γ是区域G的边界,且Γ_∈C_μ~1(0<μ<1),|λ(Z)|≠0,λ(Z)、γ(Z)_∈C_ν(Γ),1/2<ν<1。而当0≤X=1/2πΔ_Γargλ(z)相似文献