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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.

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： homoclinic solution periodic difference equation linking theorem periodic approximation

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.

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 *** this paper,we formulate an age structure model of pseudorabies virus that takes into account disease-related mortality and vertical *** find a threshold to determine the stability and existence of the *** 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 *** give detailed proofs of our theoretical results and numerical *** concluding re-marks are also provided.

关键词： Pseudorabies virus model Equilibrium Global stability Age structure

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

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

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 Department of Applied Mathematics Hunan University 410082 Changsha 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

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时滞微分方程周期解的唯一性问题

中国科学：数学 2017年第1期47卷 221-226页

作者：庾建设广州大学数学与信息科学学院广州510006

考虑时滞微分方程x′(t)=-f(x(t-1)),其中f∈C(R,R)是一个奇函数且满足xf(x)>0(x≠0).本文通过引进角速度函数以及应用移动直角三角形技巧,给出了上述方程至多有一个周期为4的Kaplan-Yorke型周期解的充分条件,首次改进了Nussbaum(1979)... 详细信息

考虑时滞微分方程x′(t)=-f(x(t-1)),其中f∈C(R,R)是一个奇函数且满足xf(x)>0(x≠0).本文通过引进角速度函数以及应用移动直角三角形技巧,给出了上述方程至多有一个周期为4的Kaplan-Yorke型周期解的充分条件,首次改进了Nussbaum(1979)的唯一性结果.最后,本文还举例给出了定理的应用.

关键词：时滞微分方程 Kaplan-Yorke型周期解 Hamilton系统角速度函数移动三角形技巧

Modulation of first-passage time for gene expression via asymmetric cell division

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International Journal of Biomathematics 2019年第5期12卷 97-114页

作者： Kunwen Wen Lifang Huang Qi Wang jianshe yu School of Mathematics Jiaying University Meizhou 514015P.R.China Center for Applied Mathematics Guangzhou University Guangzhou 510006P.R.China School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou 510320 P.R.China

How to balance the size of exponentially growing cells has always been a focus of *** experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell divi-sion in prokaryote is not completely *** timing of cell division is essentially random because gene expression is stochastic,but cells seen to manage to have precise timing of cell division *** the inter cellular variability of gene expression has attracted much attention,the randomness of event timing has been rarely *** our analysis,the timing of cell division is formulated as the first-passage time (denoted hy FPT) for time-keeper protein’s level to cross a critical threshold firstly,we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell *** results of numerical simulation show that the regulatory factors (division rate,newborn cell size,exponential growth rate and threshold) have significant influence on the mean and noise of *** also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT,the larger the exponential growth rate is,the smaller the mean and noise of FPT will be;and the larger the threshold value is,the higher the mean of FPT is and the lower the noise *** addition,compared with symmetric divi sion,asymmetric division can reduce the mean of FPT and improve the noise of *** summary,our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.

关键词： Asymmetric cell division first-passage time mean and noise