Weak Solutions of Monge-Ampére Type Equations in Optimal Transportation

This paper concerns the weak solutions of some Monge-Ampére type equations in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampére type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.     

一类二阶迭代微分方程的周期解

利用拓扑度理论研究了一类二阶迭代泛函微分方程x(t) g(x(x(t)))=f(t,x(t),x(t))的周期解的存在性,得出了周期解存在的充分条件.     

EXISTENCE OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

0 IntroductionRecently, the study of ordinary differential equations in a Banach spacehas been developed extensively by using the strong topology, see [2],13],[4]. Atpresent, however, there is no reference or paper which systematically studiesweak solutions of the Cauchy problem of ordinary differential equation in theweak topology. In references [l],15],[7] and [8], several results of weak solutionsare proved. In this paper, we shall give the other results of weak solutions,some of which are…     

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.     

EXISTENCE OF WEAK SOLUTIONS FOR A DEGENERATE GENERALIZED BURGERS EQUATION WITH LARGE INITIAL DATA

11MroduCtlonIn this paper we will investigate the global exlstence ofwe欢 solutions to a de欧nerate辟nerajlzed Bur驴d equatllJll in the formut ＋(。侧。＝t。。。,x E R‘,t＞0(1．1)with the initial data刚,x)一。。卜 卜)(1．1)is not only a means to study hxPerbolic conser、nonl。s[1,2]but also the mathematicalmodel of*the*、 propapatlon offinlt。。plltude sound w。es in、i劝l。area ofduct(see[3;4]),where u is an roustlc vrable,with the linear effects of chang6s!n the duct area taken out;andt I…     

一类矩阵方程的正交对称解及其最佳逼近

1引言设Rn×m表示所有n×m实矩阵集合,I表示单位矩阵,AT表示矩阵A的转置矩阵, ORn×n={P|PTP=I)表示列正交矩阵集,SORn×n={P|PT=P,P2=I}表示对称正交对称矩阵集．如无特别说明,本文中的矩阵P均指这类对称正交对称矩阵．在Rn×m上定义内积为     

EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS

In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.     

线性规划最优解集的表现

文献［１］讨论了有无穷多最优解的线性规划问题，并利用最优单纯形表格的检验数给出线性规划有无穷多最优解的判别法，本文利用最优基可行解的凸组合及最优极向的非负线性组合给出线性规划最优解集的表现，从而把线性规划最优解集的几何特征阐释清楚．     

非均匀介质中波动方程的部分不变解

讨论了来自于非均匀介质中波动方程的部分不变解的存在性，证明了在波速满足适当的条件下部分不变解是存在的，并得到了部分不变解。     

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS

This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.     

一类复函数方程组的亚纯解

本文研究了一类复函数方程组的亚纯解的存在性问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关方程组的亚纯解变成了有理解的一个主要结论,将复函数方程的某些结果推广至复函数方程组中.     

中立型时滞差分方程的振性与正解存在性

本文研究了一类中立型时滞差分方程的振动性和正解存在性，获得了该方程所有解振动的“Sharp”条件及存在正解的一个充分条件．     

一类修正的Navier—Stokes方程组Neumann边值问题的弱解

讨论一类修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ型方程组Ｎｅｕｍａｎｎ边值问题的可解性及解的性质。     

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlineax transformation which is a functionof density and entropy the corresponding problem can be reduced to a semilinear ellipticequation with a nonlinear source term consisting of a power function, for which the classical     

复微分方程组的代数解

本文研究了一类复微分方程组的代数解的存在问题.利用最大模原理和Nevanlinna值分布理论,得到了一个结论,推广和改进了一些文献的结果,例子表明结论精确.     

中立型时滞差分方程解的渐近性

给出了中立型时滞差分方程△（ｘｎ＋ｐｘｎ－ｋ）＋ｑｎｆ（ｘｎ－ｍ）＝０一切非振动解趋于零（ｎ→∞）的充分条件，证明了方程（Ｅ）一切解振动的两个新的定理。     

用矩阵分解求解线性矩阵方程的最优解

In this paper,the following problems are considered     

TIME OPTIMAL IMPLUSE CONTROL PROBLEMS

ＴＩＭＥ　ＯＰＴＩＭＡＬ　ＩＭＰＬＵＳＥ　ＣＯＮＴＲＯＬ　ＰＲＯＢＬＥＭＳＴＩＭＥＯＰＴＩＭＡＬＩＭＰＬＵＳＥＣＯＮＴＲＯＬＰＲＯＢＬＥＭＳ￥ＸｕＺｏｎｇｙｕｎ（ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ａｃｌａｓｓ...     

广义特殊Tzitzeica-Dodd-Bullough类型方程的行波解

本文研究了广义特殊Tzitzeica-Dodd-Bullough类型方程,利用动力系统分支理论方法,证明该方程存在周期行波解,无界行波解和破切波解,并求出了一些用参数表示的显示精确行波解.     

POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions: \"subsolution (?) supersolution\",the existence and stability/instability of equilibrium solutions are obtained.