Permanence and global attractivity of an impulsive delay Logistic model

In this paper, we consider an impulsive delay Logistic model. First by mathematical analysis, we obtain the maximum and minimum values of solutions of the corresponding autonomous Logistic model. Then by applying the comparison theorem and constructing some suitable Lyapunov functionals, we discuss the permanence and the global attractivity of the model, based on the boundedness of solutions of the corresponding autonomous Logistic model. An example together with its numerical simulation is given to verify our main result.     

数值误差对能斯特方程计算结果的影响

电势和浓度通过能斯特方程相互计算时,计算结果受对方数值误差的影响。本文通过误差传递和实例研究了这种影响。结果表明：浓度误差对电势计算值的影响小,而电势误差对浓度计算值的影响大;这种现象在电子转移数较多、电势较大时更加显著。浓度为计算目标时需要重视数值误差的影响,所以代入能斯特方程的电势值应该有足够精度,或者避免使用能斯特方程,而是通过平衡常数进行计算。电势为计算目标时,浓度误差的影响较小,因此可以通过近似手段估算浓度,然后代入能斯特方程,既简化计算,又保证精度。     

SUPERCONVERGENCE OF A DISCONTINUOUS GALERKIN METHOD FOR FIRST-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS

This paper deals with the discontinuous Galerkin (DG) methods for delay differential equations.By an orthogonal analysis in each element,the superconvergence re...     

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y _n + py _n−k + q _n y _n−l = 0 for n∈ℤ⁺(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ₁(u _n,m + pu _n−k,m ) + q _n,m u _n−l,m = a ²Δ² ₂ u _{n +1, m−1} for (n,m) ∈ℤ⁺ (0) ×Ω, (2*) study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses. Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000     

Some Results on Evolutionary Equations Involving Functions of the Curvatures of the Graph

51.Introducti0nandMainResultlnthepaperL1J,Caffarelli,NirenbergandSpruckdiscussedtheDirichletproblemforthenonlinearellipticequationforunknownu=u(x):{':<;;>:,<";>:are,vxeD,(1-1)where0lsab0undedstrictlyconvexdomaininR"withsmoothboundaryare,K(u)=(K,(u),Kz(u),..',K"(u))denotestheprincipalcurvaturesofthegraph(x,u(x))andfisofaspecialnatureasinL2J'L3j.Typicalcasesoftheequationin(1.l),whichweretreatedaswellbyIvochkina[4J,isf=Sl/*(K),whereS*(K)arethee1ementarysymmetricfunctions,Recently,Ivochki…     

一阶时滞微分方程解的零点分布

Abstract. The paper gives two estimates of the distance between adjacent zeros of solutions     

分布在非齐次空间中捕食－被捕食系统的锁相振动

本文以经典的带有时滞的捕食－被捕食系统为基础，构造了一类泛函微分方程作为描述分布在由ｎ个岛屿构成的环状区域上的捕食－被捕食种群生长过程的模型．我们假设种群在最相邻的岛屿间相互迁移，以迁移率为分支参数，研究了该系统的锁相振动，给出了离散波分支的存在条件．     

Asymptotic stability in perturbed delay difference systems

Consider the delay difference system

     

On blow-up results for solutions of inhomogeneous evolution equations and inequalities

The main purpose of this work is to obtain blow-up results for solutions of the inequality