STRONGLY NONLINEAR VARIATIONAL PARABOLIC EQUATIONS WITH p(x)-GROWTH

We study the Dirichlet problem associated to strongly nonlinear parabolic equations involving p(x) structure in W_0~(1,x)L~(p(x))(Q). We prove the existence of weak solutions by applying Galerkin's approximation method.     

在空间W_0~(1，x)L~(P(x))(Q)及其共轭空间中的若干收敛性定理

本文证明了在空间W_0~(1,x)L~(p(x))(Q)及其共轭空间中三个收敛性定理.在附加较弱条件的情况下,给出了几乎处处收敛蕴含弱收敛,弱收敛蕴含强收敛.     

含临界指数的类p-Laplacian方程无穷多解的存在性

考虑如下一类含临界指数的类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=:-- |u|~(p~*-2)u+λf(x,u),u∈W_0~(1,p)(Ω),其中Ω∈R~N(N≥2)为有界光滑区域,a:R~+→R为连续函数.由于问题失去紧性,对Palais-Smale序列的分析需要一点技巧.本文利用Lions的集中紧原理,证明了相应泛函I_λ满足(PS)_c条件,再应用Clark临界点定理和亏格的性质,证明了方程无穷多解的存在性.进一步,得到当λ充分小时一个特殊的特征函数的存在性.     

几何测度空间基的研究

研究了几何测度空间中的基本对称函数μ_0,μ_1,…,μ_n和内蕴体积函数V_0,V_1,…,V_n,证明了Lⁿ上连续不变赋值函数空间中由基本对称函数构成的基{μ_0,μ_1,…,μ_n}和由内蕴体积函数构成的基{V_0,V_1,…V_n}(或均质积分构成的基{W_0,W_1,…,W_n})等价.     

一类奇异拟线性椭圆方程正解的多重性

研究奇异拟线性椭圆型方程{-div(|x|~(-ap)|▽u|~(p-2)▽u) + f(x)|u|~(p-2) = g(x)\u|~(q-2)u + λh(x)|u|~(r-2),x R~N,u(x) 0,x∈ R~N,其中λ0是参数,1pN(N3),1rpgp*=0a(N—p)/p,p*=Np/{N~pd),aa+l,d=a+l-60,权函数f(x),g(x),h(x)满足一定的条件.利用山路引理和Ekeland变分原理证明了问题至少有两个非平凡的弱解.     

用卷积定义的解析函数子类的Fekete-Szeg不等式

本文研究了一个新的解析函数子类Mλ(g,h,u,v,φ)(0≤λ≤1)的系数不等式.利用分析的方法和技巧,得到它精确的Fekete-Szeg不等式及通过分式微分定义的函数类的Fekete-Szeg不等式.所得结果推广了一些作者的相关结果.     

一类复线性微分差分方程亚纯解的唯一性

本文主要研究一类复线性微分差分方程超越亚纯解的唯一性.特别地,假设$f(z)$为复线性微分差分方程: $W_{1}(z)f''(z+1)+W_{2}(z)f(z)=W_{3}(z)$的一个有穷级超越亚纯解,其中$W_{1}(z)$, $W_{2}(z)$, $W_{3}(z)$为增长级小于1的非零亚纯函数并且满足$W_{1}(z)+W_{2}(z)\not\equiv 0$.若$f(z)$与亚纯函数$g(z)$, $CM$分担0,1,$\infty$,则$f(z)\equiv g(z)$或$f(z)+g(z)\equiv f(z)g(z)$或$f^{2}(z)(g(z)-1)^2+g^{2}(z)(f(z)-1)^2=g(z)f(z)(g(z)f(z)-1)$或存在一个多项式$\varphi(z)=az+b_{0}$使得$f(z)=\frac{1-e^{\varphi(z)}}{e^{\varphi(z)}(e^{a_{0}-b_{0}}-1)}$与$g(z)=\frac{1-e^{\varphi(z)}}{1-e^{b_{0}-a_{0}}}$,其中$a(\neq 0)$, $a_{0}$ $b_{0}$均为常数且$a_{0}\neq b_{0}$.     

Привалов定理的拓广

<正> 设Ω是 m 个实变数 u_1,…,u_m 空间中的-p 维可定向流形Ω:(?)Ω称为属于 C~e 类(e是非负的整数),如果实函数 f_1,…,f_(m-p)皆有e次连续偏微商.Ω称为平滑的,如Ω属于 C~1 类并且矩阵     

空间（Lμ^p）^m的弱Banach-Saks性质

证明了由m个Lμp空间产生的Banach向量空间（Lμp）m的弱Banach-Saks性质,其中m是自然数, 1 p 〈＋∞.当m= 1时,这就是著名的Banach-Saks-Szlenk定理.运用该性质,还给出了定义在向量空间Rm的一个凸集上的非负连续凸函数与取值在空间（Lpμ）m的一个弱紧子集中的向量值函数的复合函数的积分不等式.当这些向量值函数属于由m个Lμ∞空间产生的积空间（Lμ∞）m的一个弱＊紧子集时,类似的积分不等式还是成立的.     

一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|~(α-1)u″)′+q(t)|u|~(β-1)u=0其中α0,β0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)0,q(t)0.当t→∞时此方程满足∫_a~∞1/((p(t))~(1/α))dt=∞的特殊非振动解存在的充分必要条件.     

On K3 of Witt Vectors of Length Two Over Finite Fields

We prove that for W₂ the Witt vectors of length two over the finite field , we have in characteristic at least 5 and for (3,f) = 1. The result is proved by using the identity and calculating the right term with a group homology spectral sequence. Some information on the spectral sequence is achieved by using the action of the outer automorphism of SL on the homology groups and recent results on K-groups of local rings and the ring of dual numbers over finite fields.     

Maximal Inequalities for the Best Approximation Operator and Simonenko Indices

In an abstract set up, we get strong type inequalities in L~(p+1) by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequalities for maximal functions associated to best Φ-approximation operators in an Orlicz space L~Φ.     

Order comparison of norms of polynomials in regions of the complex plane

For an arbitrary Jordan region G, inequalities are obtained which relate the norm with the norms and of a polynomial P_n(z) of degree n.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1277–1280, September, 1991.     

Conformally Invariant Functionals on the Riemann Sphere

The main aim of this work is to establish new inequalities for the Grunsky coefficients of univalent functions. For this purpose, we apply results from the theory of problems on extremal decomposition. To obtain inequalities for the Grunsky coefficients of a function , we apply a solution of the problem on the maximum of a conformal invariant (this invariant, in its turn, is connected with the problem on extremal decomposition of into a family of simply connected and doubly connected domains). In contrast to similar inequalities obtained from the Jenkins general coefficient theorem, the inequalities established in this work are valid without any restrictions on the initial coefficients of the expansion of a function . Bibliography: 6 titles.     

Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent

In this paper, we are concerned with a show the existence of a entropy solution to the obstacle problem associated with the equation of the type :$\begin{cases}Au+g(x,u,∇u) = f & {\rm in} & Ω \\ u=0 & {\rm on} & ∂Ω \end{cases}$where $\Omega$ is a bounded open subset of $\;\mathbb{R}^{N}$, $N\geq 2$, $A\,$ is an operator of Leray-Lions type acting from $\; W_{0}^{1,\overrightarrow{p}(.)} (\Omega,\ \overrightarrow{w}(.))\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'(.)} (\Omega,\ \overrightarrow{w}^*(.))$ and $\,L^1\,-\,$deta. The nonlinear term $\;g\,$: $\Omega\times \mathbb{R}\times \mathbb{R}^{N}\longrightarrow \mathbb{R} $ satisfying only some growth condition.     

典型實照函數的最小?妥钚∑

<正> 1.如果函數f(z)在包含實軸土某一區間的區域B中是正則的,f(z)在此實軸區間上取實值.在區域B的其餘地方f(z)與(z)同符號;即     

平均曲率的一个积分等式

<正> 在Соболв空间W_(2,0)~2(Ω)中,假定区域Ω的边界Ω是充分光滑的.本文给出了同Ω的平均曲率有关的一个积分等式,并指出了这个等式的一点应用. 设Ω是R~n中的一个单连通域,边界Ω是及R~n中的n-1维Riemann流形.R~n     

劳勃生的特殊星像函数和特殊凸像函数

<正> 设函数w在单位圆 E_z:|z|<1上是正则的.假如f(z)在 E_z上是单叶的,那末 D_f=f(E_z)是 w 平面上单叶的区域.记这种单叶函数f(z)的全体为 S_p,S_1=S.若 D_f 以原点 w=0 为星形中心,就是说若 w_0∈D_f则缐段■整个地落在区域 D_f 中,称这种函数 f(z)是 E_z 中的星像函数,其特徵是在 E_z     

Weighted Inequalities for Monotone Functions

Weighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi-linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which $ \int\limits_0^\infty {f(x)^p w(x)dx \le C \int\limits_0^\infty {({\textstyle{1 \over x}}\int\limits_0^x f)^p } v(x) dx,} $ for nondecreasing functions f and 1 ≦ p < ∞.     

Whitney property in two dimensional Sobolev spaces

For , we prove that all the functions of satisfy the Whitney property; i.e., if is such that (in the sense of capacity) on a connected set , then is constant on .