一类双重退化抛物方程局部解的存在性

This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate p- Laplace equation(p＞2) u_t-div(b(x,t,u)|▽u|~(p-2)▽u)=f(x,u,t). The initial-boundary value problem in a bounded domain of R~N is considered under mixed boundary conditions.The existence of local-in-time weak solutions is obtained.     

热传导方程的均匀化方程的混合元方法

用混合有限元方法讨论稳态热传导问题的均匀化方程.给出了一种矩形剖分下的混合元格式,该格式具有各向异性特征,即剖分不满足正则性条件时也收敛,应用各向异性插值定理给出了误差分析.     

一类抛物型方程边界条件的均匀化模型及证明

设伪抛物问题边界 Ω =Γ可表为Γ =Γ0 ∪Γ1,对任意ε>0 ,将Γ1分为Γε1和Γε1,并在其上给出不同的边界条件 ;讨论了几种当Γε1的每一连通分支的直径或沿某方向的直径随ε趋于零而趋于零时的相应解的极限性态 .     

椭圆问题的非线性边界条件均匀化

在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。     

非线性椭圆方程等值面边值问题熵解的存在性和正则性

本文研究了非线性椭圆方程等值面过值问题摘解的存在性和正则性,并改进了以前的结果。     

伪抛物问题非线性边界条件的均匀化

对于伪抛物问题讨论了当边界条件是非线性时的均匀化问题;设边界a∩=Г可表为Г=Г。UГ1,对任意ε＞0,将Г1分为Г1分为Г1和Г1,并在其上给出不同的边界条件;讨论了几种当Г1的每一连通分支的直径或沿某方向的直径随ε趋于零而趋于零时的相应解的极限性态．     

二阶离散边值问题的一个存在性定理

作者利用监界点理论中的山路引理研究了一类非线性二阶差分方程边值问题解的存在性,获得了该边值问题有解的一个充分条件.     

一类拟线性抛物方程的均匀化

本文研究具有振荡系数的二阶抛物方程δｔｂ（ｕ）－δｘｉ（αｉｊ（ｘ／ε）δｘｊｕ＋αｉ（ｂ（ｕ）））＝ｆ（ｂ（ｕ））的渐近性态。由于函数ｂ（ｕ）的导函数ｂ‘（ｕ）允许为非线性函数，并可在ｕ＝０处退化，研究了均匀化问题通常的能量方法在这里行不通。     

各向异性的椭圆方程障碍问题弱解的局部正则性(英文)

本文在适当的假设下研究各向异性的非线性椭圆方程-divA(x,Du)=B(x,u,Du),使用各向异性的逆Hlder不等式和Sobolev不等式,得到椭圆方程障碍问题的弱解的局部正则性,推广了A-调和方程-divA(x,Du)=0的相关结果.     

p-Laplace方程混合边值问题正解的存在性

运用锥上的不动点理论，讨论了p—Laplace方程混合边值问题正解的存在性。     

Existence Theory for an Arbitrary Order Fractional Differential Equation with Deviating Argument

In this paper, we are concerned with the existence criteria for positive solutions of the following nonlinear arbitrary order fractional differential equations with deviating argument

Local and Global Existence for an Aggregation Equation

The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005 Bodnar , M. , Velazquez , J. J. L. ( 2005 ). Derivation of macroscopic equations for individual cell-based models: a formal approach . Math. Methods Appl. Sci. 28 ( 15 ): 1757 – 1779 .[Crossref], [Web of Science ®] , [Google Scholar]; Holm and Putkaradze, 2005 Holm , D. D. , Putkaradze , V. ( 2005 ). Aggregation of finite size particles with variable mobility . Phys. Rev. Lett. 95 : 226106 . [Google Scholar]; Mogilner and Edelstein-Keshet, 1999 Mogilner , A. , Edelstein-Keshet , L. ( 1999 ). A non-local model for a swarm . J. Math. Biol. 38 ( 6 ): 534 – 570 .[Crossref], [Web of Science ®] , [Google Scholar]; Morale et al., 2005 Morale , D. , Capasso , V. , Oelschläger , K. ( 2005 ). An interacting particle system modelling aggregation behavior: from individuals to populations . J. Math. Biol. 50 ( 1 ): 49 – 66 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Topaz and Bertozzi, 2004 Topaz , C. M. , Bertozzi , A. L. ( 2004 ). Swarming patterns in a two-dimensional kinematic model for biological groups . SIAM J. Appl. Math. 65 ( 1 ): 152 – 174 (electronic) .[Crossref], [Web of Science ®] , [Google Scholar]; Topaz et al., 2006 Topaz , C. M. , Bertozzi , A. L. , Lewis , M. A. ( 2006 ). A nonlocal continuum model for biological aggregation . Bull. Math. Biol. 68 ( 7 ): 1601 – 1623 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).     

不动点理论与里卡提方程两个正周期解的存在性

利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.     

Existence and Multiplicity Results for the Nonlinear Klein-Gordon Equation

In this work, we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear one-dimensional Klein-Gordon Equation. We prove that the existence of positive solutions is equivalent to the solvability of a scalar equation 2F(M) = 1, where F is a real function depending on V. Moreover, we prove some existence and multiplicity results for the Dirichlet problem in the superlinear case.     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.     

Existence and Multiplicity Results for a Degenerate Elliptic Equation

The goal of this paper is to study the multiplicity result of positive solutions of a class of degenerate elliptic equations. On the basis of the mountain pass theorems and the sub- and supersolutions argument for p-Laplacian operators, under suitable conditions on the nonlinearity f（x, s）, we show the following problem：-△pu=λu^α-a（x）u^q in Ω,u│δΩ=0 possesses at least two positive solutions for large λ, where Ω is a bounded open subset of R^N, N ≥ 2, with C^2 boundary, λ is a positive parameter, Ap is the p-Laplacian operator with p 〉 1, α, q are given constants such that p - 1 〈α 〈 q, and a（x） is a continuous positive function in Ω^-.     

Existence and Uniqueness of Periodic Solution of Delayed Logistic Equation and Its Asymptotic Behavior

In this paper, our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior. In case the coefficients are periodic, we give some sufficient conditions for the existence and uniqueness of periodic solution. Furthermore, we also study the effect of time-delay on the solution.     

Existence Theorem of Global Solutions for Monge-Ampere Equation

ＥｘｉｓｔｅｎｃｅＴｈｅｏｒｅｍｏｆＧｌｏｂａｌＳｏｌｕｔｉｏｎｓｆｏｒＭｏｎｇｅ－ＡｍｐｅｒｅＥｑｕａｔｉｏｎｈｏＬｉｊｉａｎｇ（鹿立江）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｔｉａｎｊｉｎ，３００２２２）...