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A solution to parabolic system with the fractional Laplacian

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Applied math.matics(A Journal of Chinese Universities) 2009年第2期24卷 184-190页

作者： FANG Lin FANG Dao-yuan Dept. of math. Zhejiang Univ. Hangzhou 310027 China

The existence of a solution to the parabolic system with the fractional Laplacian （-△） α/2, α 〉 0 is proven, this solution decays at different rates along different time sequences going to infinity. As an application, the existence of a solution to the generalized Navier-Stokes equations is proven, which decays at different rates along different time sequences going to infinity. The generalized Navier-Stokes equations are the equations resulting from replacing -△ in the Navier-Stokes equations by （-△）^m, m〉 0. At last, a similar result for 3-D incompressible anisotropic Navier-Stokes system is obtained.

关键词： parabolic system fractional Laplacian decay rate

Quaternary quasi-cyclic codes

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Applied math.matics(A Journal of Chinese Universities) 2008年第3期23卷 359-365页

作者： PEI Jun-ying ZHANG Xue-jun Dept. of math. Soochow Univ. Suzhou 215006 China

Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of A^n, where A = Z4[x]/（x^m - 1）. In the case of m being odd, all quasi-cyclic codes are shown to be decomposable into the direct sum of a fixed number of cyclic irreducible A-submodules. Finally the distinct quasi-cyclic codes as well as some specific subclasses are enumerated.

关键词： quasi-cyclic code primary component type

A CHARACTERIZATION OF THE SOLUTIONS OF p-ORDER FEIGENBAUM'S FUNCTIONAL EQUATION WITH TOPOLOGICAL ENTROPY

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Acta math.matica Scientia 1996年第1期16卷 38-43页

作者：廖公夫 Dept. of math. Jilin Univ. Changchun 130023 China

Let f be a continuous anti-unimodal solution of a p-order Frigenbaum's dunctioal equation.A criterion is given to determine whether or not the topological entropy of j is *** a continuous anti-unimodal solution of 4-o... 详细信息

关键词： Feigenbaum's functional equation Anti-unimodal solution Topological entropy.

TWO-DIMENSIONAL SINGULAR INTEGRAL EQUATIONS OF THE HYPERCOMPLEX FUNCTIONS

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Acta math.matica Scientia 1996年第1期16卷 44-50页

作者：刘春根 Dept. of math. Nankai Univ. Tianjin 30071 China

In this paper, it is considered for some two-dimensional singular integral equations of the hypercomplex functions in the Douglis sense. In some special cases, the Fredholm' conditions and index formula of such equati... 详细信息

关键词： singular integral equation hypercomplex function index formula

PARACOMMUTATORS ON PRODUCT SPACES

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Acta math.matica Scientia 1993年第1期13卷 39-55页

作者：李春林鹏彭立中 Dept of math. Beijing University Beijing 100871 China

The boundedness and the Schatten-von Neumann properties of paracommutators on product spaces are studied. They turn out to be characterized by the membership of their symbols in the BMO space and the Besov spaces on p... 详细信息

关键词：乘积空间仿交换子 BMO空间 Bessov空间

ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM

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Acta math.matica Scientia 1988年第4期8卷 389-398页

作者：王怀忠,周钦德 Dept. of math. Jilin University Changchun china Dept. of math. Jilin University Changchun china

In this paper we study the Robin boundary value problem with a small parameterεy″=f(t, y, ω（ε）y′, ε),a0y（0） +b0y′（0）=（ε）, a1y（1）+b1y′（1）=η（ε）,where the function ω（ε） is continuous on ε≥0 with ω（0）=0. Assuming all known functions are suitably smooth, f satisfies Nagumo's condition, fy>0, a_t2-b_t2≠0, （-1）iaibi≤0 （i=0, 1） and the reduced equation 0=f（t, y, 0, 0） has a solution y（t）（0≤t≤1）, we prove the existence and the uniqueness of the solution for the boundary value problem and givo an asymptotic expansion of the solution in the power ε1/2which is uniformly valid on 0≤t≤1.

关键词： ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

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Applied math.matics(A Journal of Chinese Universities) 2008年第3期23卷 319-325页

作者： WEI Li SU Yong-fu ZHOU Hai-yun School of math. and Statist. Hebei Univ. of Economics and Business Shijiazhuang 050061 China Dept. of math. Tianjin Polytechnic Univ. Tianjin 300160 China Institute of Appl. math. and Mech. Ordnance Engineer. College Shijiazhuang 050003 China

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

关键词： maximal monotone operator relatively nonexpansive mapping strong convergence zero point fixed point

APPLICATIONS OF THE THREE CRITICAL POINTS THEOREM IN QUASILINEAR ELLIPTIC EQUATIONS

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Acta math.matica Scientia 1985年第3期5卷 279-288页

作者：沈尧天 ,郭信康 Dept. of math. University of Science & Technology of China Hefei China Dept. of math. Guangxi University Nanning China

In this paper, using the three critical points theorem which is presented by Chang Gongqing (张恭庆) in reference [1], we prove the following homogeneous Dirichlet problem:

关键词： ID 一夕一几一刁

Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian

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Applied math.matics(A Journal of Chinese Universities) 2008年第2期23卷 143-150页

作者： LI Xiang-feng Dept. of math. Longdong Univ. Qingyang 745000 China

This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.

关键词： p-Laplacian operator multiple positive solution four-point singular boundary value problem fixed-point theorem.