DIFFERENTIABILITY FOR THE HIGH DIMENSIONAL POLYNOMIAL-LIKE ITERATIVE EQUATION

This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian^[7] and by Kulczycki M, Tabor J.^[3] are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given.     

Interaction solutions to Hirota-Satsuma-Ito equation in (2+1)-dimensions

Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with Maple. The basic starting point is a Hirota bilinear form of the Hirota-Satsuma-Ito equation. A few three-dimensional plots and contour plots of three special presented solutions are made to shed light on the characteristic of interaction solutions.     

一类二阶m点边值问题的正解

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.     

ALMOST PERIODICITY FOR AN IMPULSIVE PURE DELAY LOGISTIC EQUATION

By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.     

关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.     

关于一类二阶矩阵方程的敏度分析

In this paper, the sensitivity of the solution for a class of quadratic matrix equation which arises in the analysis of structural systems and vibration problems is discussed. With Brouwer fixed piont theory, the perturbation of the quadratic matrix equation is analyzed and two computational perturbation bounds are derived. Then a Rice condition number of some kind of solutions is given using the analytic expansion method. Two examples are presented in the last part.     

Banach空间非线性二阶脉冲奇异积分-微分方程积分边值问题的正解

The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.     

A CLASS OF SINGULARLY PERTURBED EQUATIONS FOR LARGE PARAMETER WITH THREE TURNING POINTS

A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect res...     

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper, the boundary value problems of p-Laplacian functional differential equation are studied. By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.     

SOLITON SOLUTIONS TO AN EQUATION IN 2+1 DIMENSIONS

This paper considers a 2+1 dimensional equation. A bilinear form for the equation and its 3-soliton solutions are obtained by the Hirota method. The N-soliton solution is given in the form of pfaffian. At the same time the proof of the solutions are given.     

矩阵方程X-A~*X~qA=Q(q>0)的Hermite正定解

本文讨论了矩阵方程X-A*XqA=Q(q>0)的Hermite正定解,给出了q>1时解存在的必要条件,存在区间,以及迭代求解的方法．证明了0相似文献   

矩阵方程X+A~*X~(-q)A=I(q>0)的Hermite正定解

1.引言 本文研究矩阵方程 X+A*X-qA=I (1)的Hermite正定解,其中I是一个n×n阶单位矩阵, A是一个n×n阶复矩阵, q是实数且q>0.q=1,q=2时的方程是从动态规划,随机过滤,控制理论和统计学中推导出来的,最近已有许多人对此进行了研究(见参考文献[1,2,4]),本文我们将研究方程(1)的解的存在性和解的性质,并讨论迭代求解及迭代解的收敛性. 对于Hermite矩阵X和Y,文中X≥Y表示X-Y是半正定的,X>y表示X-Y是正定的;对于方阵M,M*表示M的共轭转置,ρ(M)表示M的谱半径,λi(M)     

Continuous iterations of dynamical maps: An axiomatic approach

In this paper, an axiomatic definition of continuous iterations of a dynamical map is provided. From the axioms that define common properties of all continuous iterations, it will be demonstrated that continuous iterations that are also derivable must satisfy a certain nonlinear differential equation, herein referred as the “Equation of Derivable Continuous Iterations”. A general solution of this equation will be obtained by means of the Laplace transform and it will be shown that derivable continuous iterations of a map must have a certain functional form. A formula for analytically calculating derivable continuous iterations of maps with at least a fixed point is provided.     

Periodic nonautonomous differential equations with noninstantaneous impulsive effects

In this paper, we study a new class of periodic nonautonomous differential equations with periodic noninstantaneous impulsive effects. A concept of noninstantaneous impulsive Cauchy matrix is introduced, and some basic properties are considered. We give the representation of solutions to the homogeneous problem and nonhomogeneous problem by using noninstantaneous impulsive Cauchy matrix, and the variation of constants method, adjoint systems, and periodicity of solutions is verified under standard periodicity conditions. Further, we show the existence and uniqueness of solutions of semilinear problem and establish existence result for periodic solutions via Brouwer fixed point theorem and uniqueness and global asymptotic stability via Banach fixed point theorem.     

Error analysis of Padé iterations for computing matrix invariant subspaces

The method of Padé matrix iteration is commonly used for computing matrix sign function and invariant subspaces of a real or complex matrix. In this paper, a detailed rounding error analysis is given for two classical schemes of the Pad’e matrix iteration, using basic matrix floating point arithmetics. Error estimations of computing invariant subspaces by the Padé sign iteration are also provided. Numerical experiments are given to show the numerical behaviors of the Padé iterations and the corresponding subspace computation.      

Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique

The paper deals with the numerical solution of the quasi-variational inequality describing the equilibrium of an elastic body in contact with a rigid foundation under Coulomb friction. After a discretization of the problem by mixed finite elements, the duality approach is exploited to reduce the problem to a sequence of quadratic programming problems with box constraints, so that efficient recently proposed algorithms may be applied. A new variant of this method is presented. It combines fixed point with block Gauss–Seidel iterations. The method may be also considered as a new implementation of fixed point iterations for a sequence of problems with given friction. Results of numerical experiments are given showing that the resulting algorithm may be much faster than the original fixed point method and its efficiency is comparable with the solution of frictionless contact problems.     

Iterative solution of two matrix equations

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations and , where is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation. Numerical results are reported to illustrate the convergence behaviour of various algorithms.

     

Coexistence in a competitor–competitor–mutualist model

This paper is concerned with a system modeling a competitor–competitor–mutualist three-species Lotka–Volterra model. By Schauder fixed point theory, the existence of positive solutions to a strongly coupled elliptic system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed and a numerical simulation is also presented. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak.     

Global solution to a generalized nonisothermal Ginzburg-Landau system

The article deals with a nonlinear generalized Ginzburg-Landau (Allen-Cahn) system of PDEs accounting for nonisothermal phase transition phenomena which was recently derived by A. Miranville and G. Schimperna: Nonisothermal phase separation based on a microforce balance, Discrete Contin. Dyn. Syst., Ser. B, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an N ⩽ 3- dimensional space setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, Sobolev embeddings, interpolation inequalities, Moser iterations estimates and results on renormalized solutions for a parabolic equation with L ¹ data are used to handle a suitable a priori estimate which allows to extend our local solutions to the whole time interval. The uniqueness result is justified by proper contracting estimates.     

Analogues of Feynman formulas for ill-posed problems associated with the Schrödinger equation

Representations of Schrödinger semigroups and groups by Feynman iterations are studied. The compactness, rather than convergence, of the sequence of Feynman iterations is considered. Approximations of solutions of the Cauchy problem for the Schrödinger equation by Feynman iterations are investigated. The Cauchy problem for the Schrödinger equation under consideration is ill-posed. From the point of view of the approach of the paper, this means that the problem has no solution in the sense of integral identity for some initial data. The well-posedness of the Cauchy problem can be recovered by extending the operator to a selfadjoint one; however, there exists continuum many such extensions. Feynman iterations whose partial limits are the solutions of all Cauchy problems obtained for various self-adjoint extensions are studied.