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Homoclinic solutions in periodic difference equations with saturable nonlinearity

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Science China Mathematics 2011年第1期54卷 83-93页

作者： ZHOU Zhan yu jianshe CHEN yuMing School of Mathematics and Information Science Guangzhou University Guangzhou 510006 China Department of Mathematics Wilfrid Laurier University Waterloo N2L 3C5 Canada

In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.

关键词：非线性差分方程饱和非线性周期解使用周期充分条件不存在性公开问题定理

BOUNDARY VALUE PROBLEM FOR A GENERALIZED LINARD EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2002年第1期17卷 31-38页

作者： LiuBing yujianshe CollegeofMath.andStatist. WuhanUniv.Wuhan430072 CollegeofMath.andEconometrics HunanUniv.Changsha410082

By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(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.

关键词： coincidence degree boundary value problem generalized Liénard equation existence.

Global asymptotic stability in a pseudorabies virus model with age structure

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Infectious Disease Modelling 2023年第3期8卷 865-880页

作者： Yining Chen yuhua Long jianshe yu College of Mathematics and Information Sciences Center for Applied MathematicsGuangzhou UniversityGuangzhou510006People's Republic of China

Pseudorabies is a highly contagious disease caused by pseudorabies virus(PRV)or suid herpesvirus 1(SuHV1),causing significant economic losses to the swine industry in countries where the disease exists.In this paper,we formulate an age structure model of pseudorabies virus that takes into account disease-related mortality and vertical trans-mission.We find a threshold to determine the stability and existence of the disease.We show that there is always a globally asymptotically stable boundary equilibrium if and only if R_(02)1+q,the boundary equilibrium is unstable and there exists a unique disease-endemic equilibrium,which is globally asymptotically stable.We give detailed proofs of our theoretical results and numerical examples.Brief concluding re-marks are also provided.

关键词： Pseudorabies virus model Equilibrium Global stability Age structure

Asymptotic Behavior of Solutions for a Class of Retarded Difference Equations

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Acta Mathematica Sinica,English Series 1998年第3期14卷 419-422页

作者： Huang Lihong yu jianshe Dai Binxiang Department of Applied Mathematics, Hunan University, Changsha 410082, China

Consider the retarded difference equation xn-xn-1=F（-f（xn）+g（xn-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）>0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.

关键词： Retarded difference equation Asymptotic behavior

Boundary value problems of discrete generalized Emden-Fowler equation

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Science China Mathematics 2006年第10期49卷 1303-1314页

作者： yu jianshe GUO Zhiming College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China

By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.

关键词： discrete generalized Emden-Fowler equation, boundary value problem, Saddle Point Theorem, discrete variational theory.

DISTRIBUTION OF ZEROS OF SOLUTIONS OF FIRST ORDER DELAY DIFFERENTIAL EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 1999年第4期14卷 375-380页

作者： Tang Xianhua\ yu jianshe Dept. of Appl. Math. Central South Univ. of Technology Changsha Dept. of Appl. Math. Human Univ. Changsha

The paper gives two estimates of the distance between adjacent zeros of solutions of the first\|order delay differential equation x′(t)+p(t)x(t-τ) =0 in the case when p(t)≥0 and ∫ t t-τ p(s)d s-1e ... 详细信息

关键词： Delay differentialequation,distance betw een adjacent zeros,estim ation

Periodic solutions of periodically perturbed functional differential equations

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Chinese Science Bulletin 1998年第23期43卷 1956-1959页

作者： Shiwang Ma Zhicheng Wang jianshe yu Huazhong Univ Sci & Technol Dept Automat Control Wuhan 430074 Peoples R China Hunan Univ Dept Math Appl Changsha 410082 Peoples R China

By using the generalized degree theory, some periodically perturbed functional differential equations have been proved to have at least one periodic solution if the associated homogeneous linear equations have no nont... 详细信息

关键词： generalized degree theory functional differential equation mixed type infinite delay periodic solution.

Stability Caused by Impulses for Delay Difierential Equations

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Acta Mathematica Sinica,English Series 1997年第2期13卷 193-198页

作者： yu jianshe (Department of Applied Mathematics,Hunan University,Changsha 410082,China)

In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses.

关键词： Delay differential equation Stability Impulse

SUFFICIENT　CONDITIONS　FOR　THE　EXISTENCE　OF　PERIODIC　SOLUTIONS　OF　A　AUTONOMOUS　DIFFERENTIAL　SYSTEM

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Acta Mathematica Scientia 1995年第2期15卷 126-135页

作者：黄立宏庚建设 Department of Applied Mathematics Hunan University Changsha 410082 China

In this paper, some sufficient conditions on the existence of non-trivial periodic solutions of the system dx/dt=e(y), dy/dt=- f(x)h(y)- g(x)are obtained, which not only generalize some known results concerning the Li... 详细信息

关键词： autonomous differental system periodic solution existence.