一类奇异半线性反应扩散方程初值问题整体解的存在唯一性及解的增长性

本文讨论如下问题其中σ>0,0<p<1,f(x))非负且f(z)∈L∞(RN),得到了整体解的存在唯一性及解的增长性.     

On the Existence and Stability of Solutions for a System of Elliptic Equations

We show, using a dual variational method developed in the paper, the existence of solutions for a system of Dirichlet problems for partial differential equations involving p– and q–Laplacian. The stability of solutions and the existence of positive solutions is considered in the superlinear case.      

On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations

In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on \delta, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.     

Reaction-Diffusion Equations in Homogeneous Media: Existence,Uniqueness and Stability of Travelling Fronts

The goal of this survey is to describe the construction and some qualitative properties of particular global solutions of certain reaction-diffusion equations. These solutions are known as travelling fronts (or travelling waves) and play an important role in the long-time behaviour of the solutions of the parabolic system. We will mainly focus on the existence of travelling wave solutions and their stability. We will also give some standard tools in elliptic and parabolic theory, which are of general interest.     

随机微分方程弱解的稳定性和存在性

本文研究了驱动项为无穷维Ｂｒｏｗｎ运动的一般Ｉｔ随机微分方程，给出了还问题的解和弱解的存在性关系，证明了在线性增长条件下，方程弱解的稳定性和存在性定理．     

具有时滞的Hopfield型神经网络的平稳周期振荡

研究一类具有周期输入的时滞Hopfield型神经网络　　ui(t)=-biui(t) ∑nj=1Tij(t)f(u(t-τ)) Ii(t)的周期振荡,利用重合度和V_泛函的方法,得到了该网络存在唯一稳定周期振荡的条件·     

具有无穷时滞的Volterra反应扩散方程组正解与有界正解的存在唯一性

本文利用Ｃ-ｈ空间理论,ＢＣ_ｈ空间理论和上下解方法研究具有无穷时滞的 Ｖｏｌｔｅｒｒａ反应扩散方程组正解和有界正解的存在唯一性,并给出有关应用的例子．     

具有无穷时滞的Volterra反应扩散方程组[1mm]正解与有界正解的存在唯一性时

本文利用Ch空间理论, BCh空间理论和上下解方法研究具有无穷时滞的 Volterra 反应扩散方程组正解和有界正解的存在唯一性, 并给出有关应用的例子.     

微分方程解的存在与惟一性的一种证明

运用Banach压缩定理可证明微分方程解的存在与惟一性.     

Multidimensional Travelling Wave Solutions to Reaction-Diffusion Equations

The existence of nonplanar travelling wave solutions to a reaction-diffusionequation in an infinite channel is studied numerically. A boundary-valueproblem is derived via the introduction of a moving coordinatesystem. It is approximated on a finite domain through the introductionof artificial boundaries and the imposition of asymptotic boundaryconditions. Stability results for the waves are obtained byusing maximum principles.     

On Existence of Solutions of Parametrized Generalized Equations

Set-Valued and Variational Analysis - In this paper we study existence of solutions to the generalized equation 0 ∈ f(p,x) + F(x), where f is a function, F is a set-valued mapping, and p is a...     

Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-differential operators and the nonlinear terms, it is shown that the general higher-order BBM equation has solitary-wave solutions. Moreover, under slightly more restrictive conditions, the set of solitary-wave solutions is orbitally stable. Here, the equation has a nonlinear part involving the polynomials of solution and its derivatives with different degrees (not homogeneous), which has not been studied before. Numerical stability and instability of solitary-wave solutions for some special fifth-order BBM equations are also given.     

关于耦合反应扩散系统解的整体存在性

利用对偶性技巧及Hoelder不等式，证明了一类耦合反应扩散系统解的整体存在性，推广了相关结果．     

On the Existence of Positive Solutions of Nonlinear Elliptic Equations

We study the existence of positive solutions of the nonlinear elliptic problem in D with u=0 on D, where and are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in ^d(d3). When g is superlinear at 0 and 0f(t)t for t(0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem.     

On the Existence of Periodic Solutions of Nonlinear Difference Equations

We obtain new sufficient conditions for the existence and uniqueness of an N-periodic solution (N is a positive integer) of a nonlinear difference equation with continuous argument of the form x(t + 1) = f(x(t)) and investigate the properties of this solution.     

中立型微分方程正解的存在性

考虑一阶具有正负系数中立型微分方程[x(t) -c(t)x(t -γ) ]+ p(t)x(t-τ) -Q(t)x(t-δ) =0 ,t≥t0 ,( )其中c,p ,Q ∈C( (t0 ,∞ ) ,R+) ,R+=( 0 ,∞ ) ,γ>0 ,t >δ≥ 0。我们获得了方程 ( )正解存在的充分条件。作为结果的推论 ,去掉了ZHANGBing_gen文 [4](《应用数学学报》1 996年第 2期 )中必需条件 ∫∞c0 p(t)dt=∞ ,其中 p(t) =p(t) -Q(t -τ+δ) ≥ 0 ,从而改进了文 [4]中相应结论。     

关于半线性椭圆型方程爆破解的存在性

文中得到半线性椭圆型方程的爆破问题解的存在性,其中或者是Rn中的有界区域,C3,C4,C5,C6是正常数,并且C5,C3（0,1）．     

有积分算子的非线性发展方程的空间周期分叉解及其稳定性*

本文研究比较一般的有积分算子的非线性发展方程的空间周期分叉解及稳定性问题。首先分别研究分叉解存在的必要条件和充分条件,然后用算子半群方法分析平衡解的稳定性,并讨论了稳定性交换原则。最后研究一个应用例子,对有指数型积分算子的情形得到具体结果。     

On the Existence of Anti-periodic Solutions for Implicit Differential Equations

This paper is devoted to anti-periodic solutions for a class of implicit differential equations with nonmonotone perturbations. The main tools in our study will be the maximal monotone property of the derivative operator with anti-periodic conditions and a convergent approximation procedure.