A Limit Theorem for Solutions of Backward Stochastic Differential Equations

1 Introduction and Preliminaries1.1 IntroductionIf the function g is Lipschitz in both variables yand z , and that ξ and (g(s,0,0))e[0,T] are squareintegrable, there exists a unique adapted and squareintegrable solution to a backward stochastic differe-ntial equation (BSDE) of type[1](1)where: g is the generator of BSDE (1); (T,ξ)areterminal conditions; (g,T,ξ) are standardparameters of BSDE (1). The unique adapted andsquare integrable solution of BSDE (1) denotesSince this kind of…     

L∞loc-Estimates for Local Solutions of Nonlinear Parabolic Equations

对一类非线性抛物方程的局部解进行本性模的估计.采用局部能量估计及Moser迭代法,对具有一定结构条件的非线性抛物方程,用解在较大区域上的积分模来估计它的本性模,而不依赖问题的初始值和边界值.     

The Stability of Runge－Kutta Methods for Systems of Delay Differential Equations

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Convergence of a New Adapting Runge－Kutta Method to Delay Differential Equations

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A Differential Continuation－Regularization Method for Solving Inverse Problems of Acoustic Wave Equations

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Existence of Nontrivial Solutions of A Nonlinear Volterra Integral Equation

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Existence of Positive Periodic Solutions for Two Species Population Growth Model

Existence and nonexistence criteria are established for the positive periodic solutions of two species pop-ulation growth with periodic delay by applying continuation theorem of coincidence degree theory.     

Existence of Two Solutions of Nonlinear m—Point Boundary Value Problems

Sufficient conditions for the existence of at least two positive solutions of a nonlinear m-points boundary value problems are established,The results are obtained by using a new fixed point theorem in cones.An example is provided to illustrate the theory.     

Existence of Solutions for p-Laplace Equations Subjected to Neumann Boundary Value Problem

The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.     

含有n个滞量的二维微分差分方程组周期解的存在性

本文研究含有n个滞量的二维微分差分方程组周期解的存在性,给出了方程组周期解周期的取值范围。     

非线性抛物型方程周期解

利用构造性方法证明了非线性抛物型方程边值问题ａ（ｕ）ｔ＝ｆ（ｕｘ）ｘ，（ｘ，ｔ）∈（０，１）×Ｒ，ｕ（０，ｔ）＝ｇ０（ｔ），ｕ（１，ｔ）＝ｇ１（ｔ），ｔ∈Ｒ的周期解的存在性，同时证明了周期解的比较原理和唯一性定理     

一类中立型微分方程部分解的表达式

本文讨论了方程a1x(t-Υ1) a2x(t-Υ2) a3x(t) b1x(t-Υ1) b2x(t-Υ2) b3x(t)=δ的部分解的表达式。     

泛函微分方程的周期解

利用泛函数微分方程的Lipschitz稳定性,讨论方程的周期解的存在性,给出几个存在定理。     

线性微分方程渐近概周期解的存在性

利用指数二分及函数的遍历性,讨论了一类线性微分方程渐近概周期解的存在性.     

一类中立型差分方程的周期解

讨论了一类中立型差分方程周期解的存在性,应用不动点定理,得到中立型差分方程周期解存在的充分条件。     

一类微分差分方程的初值问题的解

讨论了方程ax^.（t）＋bx^.（t-τ）＋cx（t）＋dx（t-τ）=0的一些初值问题的解，得到函数t^ke^aλt（k=0.1）作为初始函数应满足的充要条件，并得到解的表达式．     

二阶非线性差分方程正解的多重性

得到了一类带参数的二阶非线性差分方程(Pλ)的变分结构,证明了问题(Pλ)的解等价于泛函Jλ在Banach空间H上的临界点.应用有限维Banach空间上的临界点理论和抽象的临界点定理研究了(Pλ)解的多重性,证明了当参数在某个开区间上时,(Pλ)至少存在3个不同的正解.     

具有逐段常变量微分方程的概周期型解

利用渐近概周期微分方程的渐近概周期解,讨论了一类逐段常变量线性微分方程的概周期解的存在性.利用不动点理论给出了这类方程对应的非线性微分方程的渐近概周期解存在的条件.     

具有共振和无界非线性项中立型微分方程的周期解

利用拓扑度理论讨论了一类具有共振和无界非线性项中立型微分方程周期解的存在性,应用于Duffing方程获得了其周期解存在条件．