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NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

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Applied mathematics and Mechanics(English Edition) 2002年第10期23卷 1170-1175页

作者： Pakize Temtek 1, Aydn Tiryaki 2 (1 department of mathematics, Faculty of Arts and Science, Erciyes University, 38039, Kayseri, Turkey 2.department of mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar 06500 Ankara, Turke department of mathematics Faculty of Arts and Science Erciyes University 38039 Kayseri Turkey department of mathematics Faculty of Arts and Science Gazi University Teknikokullar 06500 Ankara Turkey

Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases, som... 详细信息

关键词： differential equation nonlinear nonoscillatory solution Parhi criteria

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

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Acta Mathematica Scientia 2004年第2期24卷 228-234页

作者：马万房艮孙 departmentofmathematics BeijingNormalUniversityBeijing100875China

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So... 详细信息

关键词： Integral equations direct methods anisotropic sobolev classes

On the generalized Busemann-Petty problem

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Science China mathematics 2007年第8期50卷 1103-1116页

作者： Song-jun L~(1,2+) Gang-song LENG~1 1.College of mathematics and Computer Science,Chongqing Normal University,Chongqin 400047,China 2.department of mathematics,Shanghai University,Shanghai 200444,China College of mathematics Computer Science Chongqing Normal University Chongqin 400047 China department of mathematics Shanghai University Shanghai 200444 China

The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in ? n with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative if i > 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang’s specific affirmative answer to the generalized Busemann-Petty problem.

关键词： star body cross i-section dual mixed volume Radon transform 52A30 52A40

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

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Acta Mathematica Scientia 2010年第3期30卷 713-725页

作者：曾宪忠刘振海 department of mathematics and Computational Science Hunan University of Science and Technology department of mathematics Central South University

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

关键词： Degenerate parabolic equations exterior domains -inhomogeneous dirichlet boundary conditions critical exponent blow-up global existence

PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

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Acta Mathematica Scientia 2008年第3期28卷 573-587页

作者：陈国旺薛红霞 department of mathematics Zhengzhou University department of mathematics and Physics Zhengzhou Institute of Aeronautical Industry Management Zhengzhou 450015 China

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

关键词： The generalized cubic double dispersion equation Cauchy problem existence and uniqueness of global solution nonexistence of global solution

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

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Acta Mathematica Scientia 2010年第3期30卷 810-818页

作者：周惊雷李庆国 College of mathematics and Econometrics Hunan University department of mathematics Hunan University of Arts and Science

Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain：（i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.

关键词： Complete lattice Heyting algebra linear system minimal covering

Some Endpoint Estimates for the Multiplier Operator

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Journal of Mathematical Research with Applications 2012年第3期32卷 337-345页

作者： Xiaoli CHEN 1,2 1.department of mathematics,Jiangxi Normal University,Jiangxi 330022,P.R.China 2.department of mathematics,Zhejiang University,Zhejiang 310027,P.R.China department of mathematics Jiangxi Normal University Jiangxi 330022

In this paper,the author proves that Multiplier operator is bounded on BMO（R~n）,LMO（R~n） and CBMOρ,λ（R~n）respectively if some concellation conditions are satisfied.

关键词： multiplier operator BMO space LMO space λ-central BMO space.

Dynamics of Two Extensive Classes of Recursive Sequences

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Journal of Mathematical Research and Exposition 2010年第5期30卷 929-935页

作者： Bin ZHAO1,2 1.department of mathematics,Northwest Agriculture & Forestry University,Shaanxi 712100,P.R.China 2.department of mathematics,Northwest University,Shaanxi 710127,P.R.China department of mathematics Northwest Agriculture & Forestry University Shaanxi 712100

We investigate the dynamics of two extensive classes of recursive sequences：Xn＋1 =c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）/c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）and Xn＋1c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）/c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）We prove that their unique positive equilibrium 5 = 1 is globally asymptotically stable. And a new access is presented to study the theory of recursive sequences.

关键词： recursive sequence equilibrium dynamics.

ASYMPTOTIC BEHAVIOR FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

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Acta Mathematica Scientia 2010年第5期30卷 1696-1708页

作者：毛明志李志民 School of mathematics and Physics China University of Geosciences department of Applied mathematics and Physics Anhui Institute of Science and Technology

In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point ＂environment viewed from the particle＂, under General Kalikow＇s Condition, we show the law of large numbers （LLN） and central limit theorem （CLT） for the escape speed of random walk.

关键词： random walk random environment central limit theorem law of large numbers renewal structure