OSCILLATION CRITERIA FOR ODD-ORDER DELAYED DIFFERENCE EQUATIONS

In this paper,we obtain some oscillation criteria to an odd-order delayed difference equation.     

高阶中立型时滞差分方程解的振动性

研究了一类具有变系数的高阶中立型时滞差分方程解的振动性，给出了其有界解振动的两个充分条件。     

具连续变量的高阶中立型时滞差分方程的振动性

In this paper, we study oscillation of solutions for a class of high order neutral delay difference equations with variable coefficients -τm [x(t) - c(t)x(t - τ)] = (-1)mp(t)x(t - σ), t ≥ t0 0. Some sufficient conditions are obtained for bounded oscillation of the solutions.     

自治时滞微分方程的线性化振动性

研究了非线性时滞微分方程的线性化振动性。     

Oscillation of Nonlinear Delay Impulsive Differential Equations and Inequalities

The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. In particular, the conditions are necessary and sufficient if the equations and inequalities are autonomous.     

具有变系数的二阶中立型时滞差分方程

本文研究二阶中立型时滞差分方程△２（ｘｎ－ｃｎｘｎ－ｍ）＝ｐｎｘｎ－ｋ，ｎ≥ｎ０（＊）的振动性与非振动性．其中，ＣｍＰｍ均为实数，ｐｍ≥０，Ｐｎ０，ｎ≥ｎ０，ｍ，ｋ，ｎ０是给定的非负整数，且ｍ≥１，△为向前差分算子：△Ｘｎ＝Ｘｍ＋１－Ｘｎ我们证明了：若Ｃｍ≥０，则方程（＊）总存在一个无界正解，也给出（＊）的一切有界解振动的若于充分条件及充分必要条件．     

具有变系数的二阶中立型差分方程

研究一类具有变系数的二阶中立型时滞差分方程 △τ^2[x（t）-c（t）x（t-τ）]=p（t）x（t-σ），t≥t0〉0 的解的振动性，给出了该类方程一切有界解振动的几个充分条件．     

具有变系数的二阶中立型差分方程的有界振动

研究一类具有连续变量的二阶中立型时滞差分方程，给出了该类方程一切有界解振动的几个充分条件.     

具连续变量的偶数阶中立型差分方程的振动性

研究具有连续变量的偶数阶中立型时滞差分方程的解的振动性,给出了有界解振动的几个充分条件.     

Oscillatory and Asymptotic Behavior for Second Order Quasilinear Difference Equations

1 IntroductionConsider the second order quasilinear difference equationA(g(Ay.--l)) + f(n,y.) = 0, for n E N(no), (l'l)where A is defined by Ay. = Vn+1--yn, n E N(no) = {no, no + 1,'' }, nO E N = {l, 2,'. }.The following hold throughout the paPer:(H0) (i) g: R-R is a continuous increasing fUnction with propertiessgng(y) = sgny) g(R) = R;(il) f: N(no) x R--+ R is continuous as a function of y E R;(iii) yf(n,y) > 0 for n E N and y / 0.By a solution of the equation (1.l) we mean a non…     

具正负系数的二阶中立型时滞差分方程的振动和非振动准则

研究了一类具有正负系数的二阶非线性中立型时滞差分方程的振动性,利用Banach空间的不动点原理,结合Riccati变换,获得了该类方程存在非振动解的一些新的准则,并同时得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

OSCILLATION FOR A CLASS OF LOGISTIC EQUATIONS

The oscillation of a delay difference equationis studied and the necessary and sufficient condition for all positive solutions of (E) to oscillate about its positive equilibrium is obtained.     

OSCILLATION CRITERIA FOR CERTAIN NONLINEAR DIFFERENCE EQUATIONS

1 IntroductionIn a number of recent papers [l-61 oscil1ation of solutions of second ordernonlinear difference equations has been investigated. ln this paper, we studythe oscil1atory behavior of solutions of the second order nonlinear differenceequationA(r.--lAx.--l) p.f(x.) = 0, n = l, 2,'' (1)where the difference operator a is defined by Ax. = xn 1 -- xn) n = 1, 2,' ')and the functions r, p, f are to be specified in the following text. By a solutionof Eq.(1), we mean a real sequence x = …     

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     

双曲型时滞偏差分方程解的振动性

本文主要讨论了双曲型时滞偏差分方程(?)的所有解振动的充分必要条件和振动性的判别准则,其中ａ－１≠０,ｐ＋ａ＞０,ｑ_ｉ是实数,ｋ_ｉ,ｌ_ｉ是非负整数,ｕ是一个正整数,ｉ＝１,２,…,ｕ.     

On an approach to the analysis of oscillatory solutions of nonlinear delay difference equations

The objective of this article is to establish an oscillation criterion for all solutions of nonlinear difference equation where $r(\eta )$ is a sequence of nonnegative real numbers and $\phi (\eta )$ is not necessarily monotone sequence. Also, an example is presented to illustrate the significance of the main result.     

二阶中立型变时滞差分方程解的振动性

研究了二阶中立型变时滞差分方程Δ2(xn+pxn-l)+qnf(xσ(n))=0解的振动性,获得了该类方程全部非平凡解振动的三个定理.所得结果将二阶中立型差分方程已有的振动性的相应结论推广到了二阶中立型变时滞差分方程.     

一类非线性二阶差分方程解的振动性

本文建立了非线性二阶差分方程的若干振动准则,所得结果改进了文［５］中相应的定理．