离子声波方程的初值问题

本文讨论由Ott E.等建立的机械模型,并给出了该模型初值问题存在整体性弱解的证明。     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM

Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.     

用初等行变换求线性矩阵方程的通解

本文通过建立通解矩阵的概念 ,给出了用初等行变换求线性矩阵方程 Am× n Xn× s=Bm× s的通解的方法 .     

The solutions to some operator equations with corresponding operators not necessarily having closed ranges

In this paper, we study the solvability of the operator equations in the general setting of infinite-dimensional Hilbert space with corresponding operators no necessarily having closed range. We get the necessary and sufficient conditions for the existences of the solutions and obtain formulae in each case for the general selfadjoint, positive and real positive solutions to these operator systems.     

A class of discrete time generalized Riccati equations

In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings.     

渐近线性算子方程的四种类型的解

利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.     

Oscillation of neutral delay difference equations of second order with positive and negative coefficients

This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms

Asympototic Behavior of Semilinear Periodic-Parbolic Boundary Value Problem

51.IntroductionInthispaper,westudythefollowingperiodicboundaryproblemwithNeumannboundaryconditionwhereO=RNisabounddomainwithC1 '(6>o)boundary.LetSuppose'm(x,t)eFandf.,.,$)eFforthe$beIongtoaboundsubsetofR,anditissat-isfiesForthesystem(1.1)',wesupposeitsati…     

An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C

An iteration method is constructed to solve the linear matrix equation AXB=C over symmetric X. By this iteration method, the solvability of the equation AXB=C over symmetric X can be determined automatically, when the equation AXB=C is consistent over symmetric X, its solution can be obtained within finite iteration steps, and its least-norm symmetric solution can be obtained by choosing a special kind of initial iteration matrix, furthermore, its optimal approximation solution to a given matrix can be derived by finding the least-norm symmetric solution of a new matrix equation . Finally, numerical examples are given for finding the symmetric solution and the optimal approximation symmetric solution of the matrix equation AXB=C.     

The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term

We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Δu+|∇u|=p(|x|)f(u,v), Δv+|∇v|=q(|x|)g(u,v) on RN, N?3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded.     

具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解

应用拓扑度方法证明了具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题非平凡解的存在性,其中非线性项f可以不是非负的但下方有界.给出了正解存在性的两个推论,它们是非线性项f非负情形已有结论的推广.通过两个例子来说明主要结论,例子的混合边值条件包含变号系数的多点条件和变号核的积分条件.     

Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks

In this paper, we consider the axi-symmetric flow between two infinite stretching disks. By using a similarity transformation, we reduce the governing Navier-Stokes equations to a system of nonlinear ordinary differential equations. We first obtain analytical solutions via a four-term perturbation method for small and large values of the Reynolds number R. Also, we apply the Homotopy Analysis Method (which may be used for all values of R) to obtain analytical solutions. These solutions converge over a larger range of values of the Reynolds number than the perturbation solutions. Our results agree well with the numerical results of Fang and Zhang [22]. Furthermore, we obtain the analytical solutions valid for moderate values of R by use of Homotopy Analysis.     

Existence results for a quasilinear elliptic problem with a gradient term via shooting method

The main purpose of our paper is to complete and improve a theorem of Dupaigne, Ghergu and Radulescu [Lane-Emden-Fowler equations with convection and singular potential, J. Math. Pures Appliquees (Journal de Liouville, 87(2007), 563-581).] showing the existence of solution for quasilinear elliptic equations where the nonlinearity depends on x, u and gradient term. The proofs combine O.D.E. techniques and shooting arguments. Previous developments require a monotonicity of the nonlinearity, while our main result is applied to a larger class of nonlinearities.     

Differential equations with limit-periodic forcings

The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.

     

Hammerstein方程的可解定理和解集的性状

本文在ｆ（ｘ，ｕ）关于｜ｕ｜的非常系数非线性控制下研究Ｈａｍｍｅｒｓｔｅｉｎ方程的可解性和解集的性状．     

Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.     

Existence and Nonuniqueness of Solutions to a Robin Boundary Problem for Semilinear Elliptic Equations

Sufficient conditions for existence and nonuniqueness of radially symmetric solutions to the Robin boundary problem of the form Δu + a(||x||)|u|^{-p} = 0 \qquad in B ⊂ R^N \frac{∂u}{∂n} + λu = -α \qquad on ∂B are obtained.     

Optimality conditions for vector equilibrium problems

In this paper, we present the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution, globally efficient solution, and superefficient solution to the vector equilibrium problems with constraints. As applications, we give the necessary and sufficient conditions for corresponding solution to the vector variational inequalities and vector optimization problems.     

Blow-up of Solutions of a Class of Nonlinear Parabolic Equations

In this paper we give a detailed discussion about the effect of quantitative relation between p and m on the properties of the solutions to nonlinear parabolic equation u_t - (u^mu_x)_x = u^p.     

齐次平衡法和浅水波中WBK方程的精确分析解

Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan‘s, Xie‘s and Yan‘s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.