二阶非线性椭圆型微分方程振动的区域准则

本文对二阶非线性椭圆型方程∑i,jn=1Di[AijDjy]+q(x)f(y)=0建立了若干新的振动准则,所得结果仅依赖于方程在外区域Ω(?)Rn的一个区域序列的信息而有别于已知的大多数结论.     

具无限时滞的非线性积分微分方程的周期解

本文考虑具无限时滞非线性积分微分方程和其中t∈R,T≥0是常数,x∈Rn;A(t,x),C(t,s)为n×n连续的函数矩阵;f(t,x),g(t,x),b(t)是n维连续向量.本文利用线性系统的指数型二分性理论和不动点定理研究此系统,建立了保证其周期解存在性.唯一性的充分条件.得到了一些新的结果,推广了相关文献的主要结果.     

Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated.     

松弛型并行多分裂方法解非线性方程组的安全界

本文对某些非线性方程组F(x)=0,导出了一个算法,用它可以迭代建立F(x)=0的解的紧致上、下界。算法基于某些矩阵的多分裂,因此具有自然的并行性。我们证明了趋向于解的界之收敛原则,给出了参数的收敛性区域并考察了方法的收敛速度。     

一类半线性波动方程的Sobolev指数

Gaustavo Ponce与Thomas C.Sideris猜测：对一些具有特殊非线性项的半线性波动方程,如utt-△u=u^k(Du)^αx∈R^n,k∈Z^ ,ρ＝│α│≥2,其中Sobloev指数会在[n/2,n/2 1]中,他们在x∈R^3时回答了这一问题,本文在R^n(n≥4）中得到了半线性波动方程utt-△u=u^k(Du)^α（x∈R^n,k∈R^n,k∈Z^ ,p=│α│≥2）的Sobolev指数为max{n/2,(n/2-1)1-3/l-1 2},此数确实在区间[n/2,n/2 1]中,特别当ρ≤n-1时,我们得到了此半线性波动方程的Sobolev指数为n/2。     

On the numerical imbedding method

Journal of Applied Mathematics and Computing - WhenF(x) = 0 is a system of nonlinear equations, we have established the parametrizied Homotopy algorithm for solvingF(x) = 0 and some theorems for...     

Improvement of Hartman''''s linearization theorem

Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) is bounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphism of Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x = Ax. In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we prove the result of global topological linearization without any special limitation and adding any condition. Thus, Hartman's linearization theorem is improved essentially.     

异步并行非线性对称Gauss-Seidel迭代算法

1．引言考虑非线性方程组其中A＝（a。。）EL（＊”）为＊一矩阵，B＝（衬。）EL（＊”）为非负矩阵，呐X）一（p。（X。》，4（二）＝（吵k（kk》：＊一＊一为连续的对角映射，而6＝（6k）E＊一为已知向量．这里，什小：”一”均可微，但二者的导函数并不一定连续．这类方程组具有丰富的实际背景．例如，描述冰体溶解过程的著名的Stefan问题，就可归结为问题（1·1）的数值求解（见［l］）．为在多处理机系统上有效地求解问题（1．1），文山利用这类非线性方程组的特殊结构，建立了一类并行非线性Gauss—Seidel型迭代算法．为避免该算…     

一类Rn上非线性椭圆型方程正整解的存在性及其性质

以Schauder-Tychonoff不动点定理为工具,应用上、下解得方法,建立一类高维非线性椭圆型方程△u=f（x,▽u）uβ,（x∈Rn,n≥3,0〈β〈1）正整解的存在性和性质的定理,所得的结果丰富和发展了Kawano等和许兴业的结果.     

非线性椭圆方程自由边值问题球对称解的存在性

给出了如下的非线性椭圆方程自由边值问题-Δu=λu+(1+ε)u+p,x∈B Rn,u|Ω=μ,∫Ωnu=-M(1)在C[0,1]中的球对称解的存在性.并得到比上述问题更一般的非线性椭圆方程自由边值问题-Δu=h(u),x∈B Rn,u|Ω=μ,∫Ωun=-M,在C[0,1]中的球对称解的存在性,其中B为Rn中的单位球,p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε均为常数,n为正整数.     

Strichartz estimates for parabolic equations with higher order differential operators

The present paper first obtains Strichartz estimates for parabolic equations with nonnegative elliptic operators of order 2m by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-LittlewoodSobolev inequality. Some conclusions can be viewed as the improvements of the previously known ones. Furthermore, an endpoint homogeneous Strichartz estimates on BMOx(Rn) and a parabolic homogeneous Strichartz estimate are proved. Meanwhile, the Strichartz estimates to the Sobolev spaces and Besov spaces are generalized. Secondly, the local well-posedness and small global well-posedness of the Cauchy problem for the semilinear parabolic equations with elliptic operators of order 2m, which has a potential V(t, x) satisfying appropriate integrable conditions, are established. Finally, the local and global existence and uniqueness of regular solutions in spatial variables for the higher order elliptic Navier-Stokes system with initial data in Lr(Rn) is proved.     

A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems

We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions.     

ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS

ＯＮＭＯＮＯＴＯＮＥＣＯＮＶＥＲＧＥＮＣＥＯＦＮＯＮＬＩＮＥＡＲＭＵＬＴＩＳＰＬＩＴＴＩＮＧＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳ￥ＷＡＮＧＤＥＲＥＮ；ＢＡＩＺＨＯＮＧＺＨＩ（ＤｅｐａｚａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈｓｌｌｇｈａｉＵｎｉｖｅ...     

一类中立型高维周期微分系统的周期解

本文考虑中立型高维周期系统：其中（L,x）∈R×R~n,A（t,x）为连续函数矩阵,x_t∈C（[-γ,0],R~n）,x_t（θ）＝x（t十θ）,θ∈[-r,0],记C＝C（[-r,0］,R~n）,f：R×C→R~n连续,且A（t＋T,X）＝A（t,x）,T,r＞c∈R,本文用不动点方法研究此系统,得到了其周期解存在的充分性条件,所得结果推广、改进了文［1－3］中相应结论．     

函数因子法——非线性方程组求解中处理奇异问题的一种新方法

§1.引言 非线性方程组 F(x)=0,F:D?R~n→R~n (1.1)嵌入参数t,构成同伦H:[0,T]×D?R~(n 1)→R~n,使得 H(0,x~0)=0,H(T,x)=F(x),(1.2)这里T可以是有限的或 ∞,当T为 ∞时以极限过程代替求值.若 H(t.x)=0(1.3)存在连续解x(t):[0,T]→D,则非线性方程组(1.1)的解x~*=x(T).若(1.3)的解     

求解非线性方程组的连续极小化方法

1.引言 求非线性方程组 F(x)=0 (1)(F:D?R~n→R~n)的各种方法中,牛顿法最为基本.但它只有局部收敛性和半局部收敛性,而且要求DF(x)~(-1)存在.为了扩大收敛范围及克服DF(x)奇异性带来的困难,用“连续化”的思想求方程(1)的解是一个有效的途径.这方面,已有许多工作,如[3—6].本文利用常微分方程几何理论,对连续化方法进行 些探讨,给出了沿积分曲线极小化求非线性方程组(1)的解的方法.考虑如下给定函数:     

奇异点处的拟Newton方法

1.引言 假定F是R~m→R~m的可微映射,x~*∈R~m是 F(x)=0 (1.1)的解. 如果在解点处Frechet导数是可逆的,只要F′(x)具有一定的性质,就可保证Newton迭代 x_(i+1)~N=x_i~N-F′(x_i~N)~(-1)F(x_i~N) i=0,1,… (1.2)产生的点列在||x_0-x~*||适当小时二阶收敛于x~*:     

Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks

The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.     

A Constrained Optimization Approach for LCP

In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x,y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K-T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem. In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point, However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions: M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method.     

非线性波方程准确孤立波解的符号计算

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.