ASYMPTOTIC BEHAVIOR AND EXISTENCE OF POSITIVE SOLUTIONS FOR A NEUTRAL DIFFERENCE EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｅｕｔｒａｌｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎ△（ｘｎ－ｃｘｎ－ｍ）＋ｐｎｘｎ－ｋ＝０，ｎ＝Ｎ，Ｎ＋１，Ｎ＋２，…，（１）ｗｈｅｒｅｃａｎｄｐｎａｒｅｒｅａｌｎｕｍｂｅｒｓ，ｋ，ｍａｒｅｐｏｓｉｔｉｖ...     

二阶滞后型差分方程解的渐近性质

本文研究非线性差分方程 △~2x_n+q_nx_(n+1)=a_nφ(x_n+m)(x_n+k)+bn的解的渐近表示,设对应的齐次方程非振动,建立条件使方程的任意解可表成(z_n+y_n+z_no(1))的形式,其中z_n和y_n分别是对应齐次方程的主解和非主解。     

非线性中立型时滞差分方程解的渐近性

本文考虑非线性中立型差分方程△m(Xn-m 1 Pn-m 1Xn-m 1-k) f(n,Xn-l) 0解的振动性和渐近性,所得结果推广了文献中的有关定理．     

中立型时滞差分方程解的渐近性

给出了中立型时滞差分方程△（ｘｎ＋ｐｘｎ－ｋ）＋ｑｎｆ（ｘｎ－ｍ）＝０一切非振动解趋于零（ｎ→∞）的充分条件，证明了方程（Ｅ）一切解振动的两个新的定理。     

ASYMPTOTIC BEHAVIOR OFNONOSCILLATORY SOLUTIONS OF SECOND ORDER NEUTRAL NONLINEAR DIFFERENCE EQUATIONS

1IntroductionConsiderthesecondorderneutralnonlineardifferenceequationwherenEN(no)={no,no 1,'.}(noisanonnegativeinteger),AE{--l,1},AistheforworddifferenceoperatordefinedbyAx.=xu 1--xu.Inrecentyearssthequalitativepropertiesofthesolutionsofsecondorderneutraldifferenceequationswereconsideredinanumberofpapers[1--10].Allthepapersmentioned,however,alwaysassumethatqn50foralllargen.Inthispaperouraimistostudytheasymptoticbehaviorofnonoscillatorysolutionsof(l)whenqn20foralllargen.Byasolutionof(1)weme…     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.     

THE ASYMPTOTIC STABILITY REGION TO A CLASS OF HIGHER ORDER DELAY LINEAR DIFFERENCE EQUATIONS

In this paper, we establish necessary and sufficient conditions for the zero solution to a class of higher order delay linear difference equations to be asymptotically stable, which are easy to be verified and to be applied.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SOME NONLINEAR DIFFERENCE EQUATIONS

In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

二阶差分方程解的振动性与渐近性

本文研究了二阶差分方程Δ(a     

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary.     

A THEOREM OF UNIFORMLY ASYMPTOTIC STABILITY FOR DELAY DIFFERENCE SYSTEM

In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method.     

非线性时滞差分方程的全局渐近稳定性

考虑非线性时滞差分方程xn+1-xn+pnxn-k=f(n,xn-l)(*)n=1,2,…其中pn＞0,k,l∈N={0,1,2,…},f(n,x)N×R→R关于x连续,本文获得了上述方程零解全局渐近稳定的充分条件,推广了文[1]的结果.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

ON THE RATE OF CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS

1IntroductionConsiderthefollowingdifferenceequationwhereGfRxR-Riscontinuous,p:Z -R ,k;Z -Z ,p(n)5M,k(n)5k,MER ,kEZ ;ZandZ denotethesetsofintegersandnonnegativeintegers,respective1y.Forintegersaand5,a>6,wedefineZ(a,5)={a,a l,'',6},Z(a)={a,a l,'.}.Weassumethat(i)G(x,.)ismonotonenon-decreasing,(ii)G(.,y)ismonotonenon-increasing;(iii)G(x,x)=o,G(x,y)5oforx>yandG(x,y)2oforx相似文献   

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (I)

1.IntroductionLetfi=(0,l),f(x)eL'(fl),"o(x)EH'(fl)nHI(fl),op(u)=u',weconsiderthefollowinginitial-boundaryvalueproblem:Bytheusualapproach[1--4]wecangettheglobalexistenceofthesolutionof(1.1),furthermore,thesolutionof(l.l)convergestothesolutionofthefollowingstationaryproblem(1.2)ast-co.l)Th.ProjectissupportedbyChinaPostdoctoralFoundationandScienceFOundationofChinaAcademyofEngineeringPhysics.Inthispaperweprovethatthesolutionofimplicitdifferenceschemefor(1.1)convergestothesolutionofdifferenc…     

二元双阈值时滞神经网络模型解的渐近性

本文研究一类具时滞和非连续型信号函数的双阈值二元神经网络模型解的渐近性。在一定的初始函数空间内，对信号函数阈值的一些不同取值范围，证明了其解的收敛性，且明确给出了各平衡点的收敛域。     

ASYMPTOTIC BEHAVIOR OF SINGULARLY PERTURBED SOLUTION FOR A CLASS OF ROBIN PROBLEM OF NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently.     

ASYMPTOTIC BEHMIOR OF A CLASS OFNONLINEAR DIFFERENCE EQUATIONSOF nTH ORDER

IIntroductlonMuch work has been done on the asymptotlcbehavlor of*theotlcbehavlor second orderdl地rentlal equation．Some results oflt are based on the Integral Inequalities’of G。"wall－B＜bar＜type．Kong Qingkal[11 has studledthe behavior ofa classofnonllnear dl地rentlal equations ofnth order．Some people[2;3]h肌e studiedthe asymptotlc behavior of the second order nonlinear difference equations．Atpresent,papers about the asymptotlc behavior of nonlinear difference equatlons of nib order …