非线性单调型映射的广义拓扑度

本文引入(S)_ ~*型和拟(S)_ ~*型映射以及弱一次连续性概念。首先证明了拟(S)_ ~*型映射包含拟有界伪单调、伪单调、拟有界广义伪单调、弱-次连续(P)型和弱-次连续(S)_ ~*型映射。然后,利用Galerkin逼近建立了(S)_ ~*型映射和拟(S)_ ~*型映射的广义拓扑度。所得结果包含了F.E.Browder的一些主要结果。     

MAPS PRESERVING THE NORM OF THE POSITIVE SUM IN Lp SPACES

For 1

p）+be the set of positive elements in L_p with norm one.Assume that V₀:S(L_p（Ω₁）)₊→S(L_p（Ω₂）)₊ is a surjective norm-additive map;that is,‖V₀（x）+V₀（y）‖=‖x+y‖,?x,y∈S(L_p（Ω₁）)₊.In this paper,we show that V₀ can be extended to an isometry from L_p（Ω₁） onto L_p（Ω₂）.     

一类四阶边值问题的多解结果

本文研究一类弹性梁方程边值问题y(1)-α₁y+β₁y"+g(x,y,y")=e,02(0.1),而g:[0,1]×R×R→R为连续有界函数,特征对(α₁,β₁)满足α₁+(0+0.5)2π2β₁=(0+0.5)4π4及α₁+(k+0.5)2π2β₁≠(k+0.5)4π4,?k∈N     

多值（S＋）型映象的度理论

本文的目的是推广张石生和陈玉清（多值（Ｓ）型映象度理论以及不动点定理）的结果·假设Ｌ是闭稠定线性极大单调映象，Ｓ是关于Ｄ（Ｌ）的（Ｓ＋）型多值映象，我们建立具有形式Ｆ＝Ｌ＋Ｓ的多值映象的拓扑度·     

集值映象的某些重合定理

Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果.     

有界线性算子及其函数的Browder定理的判定

令H是无限维的Hilbert空间,B(H)是H上有界线性算子的全体构成的集合.称算子T∈B(H)满足Browder定理,若σ(T)σ_w(T)?π₀₀(T)或σ_w(T)=σ_b(T),其中σ(T),σ_w(T),σ_b(T)分别表示算子T的谱集、Weyl谱、Browder谱,π₀₀(T)={λ∈isoσ(T):0 相似文献   

有限非链环Fq+vFq上的2维斜常循环码

令R=F_q+vF_q是一个有限非链环,其中q是一个奇素数的方幂,v²=v.文章利用二元斜多项式环R[x,y;ρ,θ]来研究环R上的2维斜常循环码的代数结构和相关性质,其中ρ和θ是环R上的两个自同构映射.基于中国剩余定理,文章确定了环R上2维(α₁+β₁v,α₂+β₂v)-斜常循环码的生成元结构并且考虑了它们的Gray象,其中α₁+β₁v和α₂+β₂v都是环R上的可逆元.此外,文章研究了环R上2维(α₁+β₁v,α₂+β₂v)-斜常循环码的对偶码并且确定了对偶码子码的生成元结构.     

拟周期系统的Floquet理论

在这篇文章,我们对拟周期系统dx/dt=A(ω₁t,ω₂t.…,ω_mt)x (0.1)建立了Floquet理论.其中n×n方阵A(u₁,u₂,…,u_m)是u₁,u₂,…,u_m以2π为周期的周期方阵,同时假定A(u₁,u₂,…,u_m)∈Cτ,τ=(N+1)τ₀,τ₀=2(m+1),N=1/2n(n+1).我们定义了(0.1)的特征指数根β₁,β₂,…,β_n,假设下式成立:其中K(ω),K(ω,β)>0,k_μ,i_v是整数,k₁,k₂…,k_m不全为零:i2=-1.那末有拟周期线性变换,把(0.1)化为常系数的线性系统.     

二维Hardy空间维林肯型系统的极大算子（英文）

本文研究二维Hardy空间维林肯型系统的极大算子的有界性.利用原子分解方法,我们证明二维极大算子T_αf:=sup₍2^-α≤n/m≤2^α)|f*P_n,m|是从鞅Hardy空间H^p到L^p有界的,其中0 *f=₍2^-α≤n/m≤2^α)|σ_n,mf|/([(n+1)(m+1)])^1/p-2的有界性证明.通过构造反例,我们证明二维极大算子■不是从鞅Hardr空间H^p到L^p有界的,其中0

相似文献   

双挠积复Finsler流形的局部对偶平坦性

设(M₁,F₁)和(M₂,F₂)是两个强凸的复Finsler流形,λ₁和λ₂是乘积流形M=M₁×M₂上的光滑实值函数,双挠积复Finsler流形(M₁×(λ₁,λ₂) M2,F)是在乘积流形上赋予了复Finsler度量F²=λ₁²F₁²+λ₂²F₂²的复Finsler流形.本文给出了双挠积复Finsler流形是局部对偶平坦流形的充要条件.     

On the degree theory for general mappings of monotone type

Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. In his classic paper published in 1983, Browder developed a degree theory for mappings of monotone type f+T, where f is a mapping of class ₊(S) from a bounded open set Ω in a reflexive Banach space X into its dual X^∗, and T is a maximal monotone mapping from X into X^∗. This breakthrough paved the way for many applications of degree theoretic techniques to several large classes of nonlinear partial differential equations. In this paper we continue to develop the results of Browder on the degree theory for mappings of monotone type f+T. By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings.     

The degree theory for set-valued compact perturbation of monotone-type mappings with an application

Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. Hu and Parageorgiou [S.C. Hu, N.S. Parageorgiou, Generalisation of Browders degree theory, Trans. Amer. Math. Soc. 347 (1995), pp. 233–259] generalized the results of Browder [F.E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9 (1983), pp. 1–39] on the degree theory to mappings of the form f?+?T?+?G, where f is a bounded and demicotinuous mapping of class (S)₊ from a bounded open set in a reflexive Banach space X into its dual X*, T is a maximal monotone mapping with 0?∈?T(0) from X into X*, and G is an u.s.c. compact set-valued mapping from X into X*. In this article we continue to generalize and extend the results of Browder on the degree theory to mappings of the form f?+?T?+?G. By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. As an application, an existence result of solutions for generalized mixed variational inequalities is given under some suitable conditions.     

ON A SURJECTIVITY FOR THE SUM OF TWO MAPPINGS OF MONOTONE TYPE

In this paper the sum(T+S)of two nonlinear mappings is considered,where T ismaximal monotone or generalized pseudomonotone and S is generalized pseudomonotone orof type(M).By using the concepts of T-boundedness,T-generalized pseudomonotonemappings and mappings of type T--(M) introduced by the author,it is proved that(T+S) is of type (M).A new surjectivity result for multivalued pseudo A-propermappings is given.As a consequence,it is obtained that the coercive mappings of type(M)whose effective domain contains a dense linear subspace are surjectivity. In particular,the author answers affirmatively a part of Browder's question(see[1],p.70).     

The Degree of Proper Holomorphic MappingsBetween Special Domains in C^n

Let Gi be closed Lie groups of U (n), Ω i be bounded Gi-invariant domains in C^n which contains 0, and O(C^n)^Gi = C, for i = 1, 2. It is known that if f : Ω 1 → Ω 2 is a proper holomorphic mapping, and f^-1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f .     

On the Bartle-Graves theorem

The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.

     

Further on set-valued equilibrium problems in the pseudo-monotone case and applications to Browder variational inclusions

This paper deals with set-valued equilibrium problems under conditions of pseudo-monotonicity. Concepts such as strict quasi-convexity, hemicontinuity and pseudo-monotonicity for extended real set-valued mappings are introduced and applied to obtain results on the existence of solutions of set-valued equilibrium problems generalizing those in the literature in the pseudo-monotone case. Applications to Browder variational inclusions under weakened conditions are given. In particular, it is shown that the upper semicontinuity from line segments of the involved pseudo-monotone set-valued operator is not needed in the whole space when solving Browder variational inclusions.     

A Local Hlder Estimate of(K_1, K_2)-Quasiconformal Mappings between Hypersurfaces

In this paper, we prove a local H¨older estimate of(K1, K2)-quasiconformal mappings between n-dimensional hypersurfaces of Rn+1under an assumption of bounded mean curvature of the original hypersurface M. With some new ingredients of the isoperimetric inequality and the co-area formula on manifolds, we extend Simon's work of quasiconformal mappings on surfaces of R3 to the setting of n-dimensional hypersurfaces of Rn+1.     

On Economic Equilibrium Type Problems with Applications

The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow–Debreu model of economic equilibrium introduced in Naniewicz (Math Oper Res 32:436–466, 2007) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used.     

Generalized solutions of quasi variational inequalities

This paper deals with multivalued quasi variational inequalities with pseudo-monotone and monotone maps. The primary objective of this work is to show that the notion of generalized solutions can be employed to investigate multivalued pseudo-monotone quasi variational inequalities. It is a well-known fact that a quasi variational inequality can conveniently be posed as a fixed point problem through the so-called variational selection. For pseudo-monotone maps, the associated variational selection is a nonconvex map, and the fixed point theorems can only be applied under restrictive assumptions on the data of quasi variational inequalities. On the other hand, the generalized solutions are defined by posing a minimization problem which can be solved by a variant of classical Weierstrass theorem. It turns out that far less restrictive assumptions on the data are needed in this case. To emphasis on the strong difference between a classical solution and a generalized solution, we also give a new existence theorem for quasi variational inequalities with monotone maps. The main existence result is proved under a milder coercivity condition. We also relax a few other conditions from the monotone map. Due to its flexibility, it seems that the notion of generalized solutions can be employed to study quasi variational inequalities for other classes of maps as well.     

幂次为2,3,4,5的素变量非线性型的整数部分

考虑了一个混合幂次为2,3,4,5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,至少有一个λ_i/λ_j(1≤ij≤4)是无理数,那么存在无穷多素数p_1,p_2,p_3,p_4,p,使得[λ_1p_1~2+λ_2p_2~3+λ_3p_3~4+λ_4p_4~5]=p.