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EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE 被引量:12
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作者 LiBiwen ZengXianwu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第1期1-8,共8页
By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]... By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0]. 展开更多
关键词 periodic solutions competition diffusive system functional response continuation theorem of coincidence degree topological degree.
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GLOBAL ATTRACTORS OF REACTION-DIFFUSION SYSTEMS AND THEIR HOMOGENIZATION 被引量:5
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作者 ZhangXingyou HuXiaohong 《Journal of Partial Differential Equations》 2004年第1期80-88,共9页
In this paper, we study the existence of the global attractor A^ε of reaction-diffusion equation δtu^ε(x,t)=Aεu^ε(x,t)-f(x,ε^-1x;u^ε(x,t)).and the homogenized attractor ,A^0 of the corresponding homogenized equ... In this paper, we study the existence of the global attractor A^ε of reaction-diffusion equation δtu^ε(x,t)=Aεu^ε(x,t)-f(x,ε^-1x;u^ε(x,t)).and the homogenized attractor ,A^0 of the corresponding homogenized equation, then give explicit estimates for the distance between the attractor .A^ε and the homogenized attractor ,A^0. 展开更多
关键词 全局吸引子 反应扩散方程组 齐性化 存在性
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BOUNDARY VALUE PROBLEM FOR A GENERALIZED LINARD EQUATION 被引量:2
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作者 LiuBing YuJianshe 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第1期31-38,共8页
By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>... By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application. 展开更多
关键词 coincidence degree boundary value problem generalized Liénard equation existence.
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SEMI-OPENNESSAND ALMOST-OPENNESS OF INDUCED MAPPINGS 被引量:1
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作者 HuangXianjiu ZengFanping ZhangGengrong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第1期21-26,共6页
Given a mapping f between continua.Let 2f and C(f) mean the induced mappings between hyperspaces.Relations are studied under the conditions:f is semi-open(almost open,respectively),2f is semi-open(almost open,respecti... Given a mapping f between continua.Let 2f and C(f) mean the induced mappings between hyperspaces.Relations are studied under the conditions:f is semi-open(almost open,respectively),2f is semi-open(almost open,respectively) and C(f) is semi-open(almost open,respectively). 展开更多
关键词 Continuum HYPERSPACE induced mapping semi-openness almost open.
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EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS OF DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS 被引量:3
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作者 WangXiaoping HuangLihong 《Annals of Differential Equations》 2005年第1期39-51,共13页
In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring... In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring the existence, uniqueness and global stability of periodic solution. These results are helpful to design global exponential stable BAM networks and periodic oscillatory BAM networks. 展开更多
关键词 variable coefficient periodic solution global exponential stable BAM neural networks
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A CLASS OF DELAY DIFFERENCE EQUATION 被引量:1
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作者 ZhuHuiyan HuangLihong 《Annals of Differential Equations》 2005年第1期99-105,共7页
We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions an... We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation. 展开更多
关键词 difference equation asymptotic behavior CONVERGENCE PERIODICITY
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A SHOOTING METHOD FOR THE SWIFT-HOHENBERG EQUATION
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作者 TaoYoushan ZhangJizhou 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第4期391-403,共13页
Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist pe... Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<32 , there exist periodic solutions having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument. 展开更多
关键词 shooting technique Swift Hohenberg equation critical point periodic solution.
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Herz Spaces on Nilpotent Lie Groups and Its Applications
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作者 ZHUYue-ping LIDeng-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第1期74-81,共8页
In this paper, we define Herz type spaces on nilpotent Lie groups and give the boundedess of heat kernel and Riesz transform on Herz spaces.
关键词 nilpotent Lie groups Herz spaces heat kernel
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OSCILLATIONS OF A CLASS OF HIGH-ORDER LINEAR ODE WITH IMPULSES
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作者 ChenFulai WenXianzhang 《Annals of Differential Equations》 2005年第2期123-134,共12页
Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some r... Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references. 展开更多
关键词 IMPULSE OSCILLATION solution of nth-order linear differential equation with impulses
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On the Lucas Base and Computation of Counting Function Mean Value
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作者 LIHai-long LIUHua-ke 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第1期84-89,共6页
In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.
关键词 Lucas sequence Fibonacci sequence mean value counting fuction
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BEHAVIOR OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS
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作者 BinHonghua HuangLihong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第4期390-398,共9页
In this paper, the discrete-time neural network model of two neurons with piecewise constant argument is considered. Some sufficient conditions under which every solution is either periodic or convergent are obtained.
关键词 CONVERGENCE PERIODICITY difference system neural network.
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A MATRIX EQUATION FROM AN INVERSE PROBLEM OF VIBRATION THEORY
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作者 WuZhuzhu WangGuorong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第1期77-82,共6页
The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions fo... The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived. 展开更多
关键词 matrix equation symmetric matrix positive semidefinite matrix positive definite matrix generalized inverse matrix.
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THE EXISTENCE OF ALMOST PERIODIC SOLUTION FOR CELLULAR NEURAL NETWORKS WITH VARIABLE COEFFICIENTS AND DELAYS
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作者 XieHuiqin WangQuanyi 《Annals of Differential Equations》 2005年第1期65-72,共8页
In this paper, we study the problem of almost periodic solution for the cellular neural networks with variable coefficients and delays. By ingeniously importing real parameters di > 0(i = 1,2,…n) which can be adju... In this paper, we study the problem of almost periodic solution for the cellular neural networks with variable coefficients and delays. By ingeniously importing real parameters di > 0(i = 1,2,…n) which can be adjusted, we establish some sufficient conditions which ensure the neural networks exist a unique almost periodic solution, and all other solutions exponentially converge to such an almost periodic solution. 展开更多
关键词 cellular neural networks almost periodic solution EXISTENCE global exponential stability
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CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
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作者 HuangWentao LiuYirong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第2期167-177,共11页
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ... The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin. 展开更多
关键词 fifth degree system focal value singular point quantity center conditions bifurcation of limit cycles.
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