DECAYING SOLUTIONS OF DIFFERENCEEQUATIONS WITH CONTINUOUS ARGUMENTS

1IntroductionItiswellknownthatdifferenceequationisanimportantmathematicaltoolinthestudyofscienceandtechnology11,2].Recently,theoscillationandstabilityofdifferenceequationsdefinedonasubsetofintegershavebeenextensivelyinvestigatedbymanyauthors,seeforexample…     

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．     

具变时滞差分方程解的振动性

本文研究了一类具变时滞的非线性差分方程解的振动性,获得了该方程解的振动准则．将结论应用于差分方程ΔＸｎ ＋ ｐｎｘｎ－ ｋｎ ＝ ０　　ｎ ＝ ０,１,２,… （）其中ｐｎ≥０,｛ｋｎ｝是正整数数列且ｌｉｍｎ→∞｛ｎ－ ｋｎ｝＝ ∞．我们得到了方程（）振动的新的充分条件．     

OSCILLATIONS OF SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS AND DELAYS

ＯＳＣＩＬＬＡＴＩＯＮＳ　ＯＦ　ＳＯＬＵＴＩＯＮＳ　ＯＦ　ＮＥＵＴＲＡＬ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳ　ＷＩＴＨ　ＶＡＲＩＡＢＬＥ　ＣＯＥＦＦＩＣＩＥＮＴＳ　ＡＮＤ　ＤＥＬＡＹＳ　ＯＳＣＩＬＬＡＴＩＯＮＳＯＦＳＯＬＵＴＩＯＮＳＯＦＮＥ...     

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。     

具有时滞的Volterra反应扩散差分方程的稳定性

本文考虑一类时滞Volterra反应扩散差分方程的初边值问题的正稳态解的稳定性。利用上下解方法和单调迭代方法得到了每一个解趋于方程的正稳态解的充分条件。     

OSCILLATION OF NEUTRAL NONLINEAR HYPERBOLIC EQUATIONS WITH DOUBLED VARIABLE COEFFICIENTS

ＯＳＣＩＬＬＡＴＩＯＮＯＦＮＥＵＴＲＡＬＮＯＮＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳＷＩＴＨＤＯＵＢＬＥＤＶＡＲＩＡＢＬＥＣＯＥＦＦＩＣＩＥＮＴＳ￥ＬｉｕＢｉｎｇ（ＨｕｂｅｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，４３５００２）Ａｂｓｔｒａｃｔ...     

OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＡＮＤＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｈｅｎＪｉａｎｈｕａ（申建华）（ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，湖南师范大学，邮编４１００...     

时滞差分方程周期正解的存在性

本文考虑了一类非线性离散种群模型周期正解的存在性.     

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。     

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．     

具有连续变量的差分方程的振动性

本文建立了具有连续交量差分方程的振动性判据，其结果改进了文献中的某些已知结果．     

NONOSCILLATORY SOLUTIONS FOR A SYSTEM OF HIGHER-ORDER NONLINEAR NEUTRAL DELAY DIFFERENCE EQUATIONS WITH MATRIX COEFFICIENTS

By using Banach contraction principle, we obtain the global results (with respect to ||A||≠1) on the sufficient conditions for the existence of nonoscilla-tory solutions to a system of nonlinear neutral delay difference equations with matrix coefficients.     

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…     

中立型时滞差分方程的振性与正解存在性

本文研究了一类中立型时滞差分方程的振动性和正解存在性，获得了该方程所有解振动的“Sharp”条件及存在正解的一个充分条件．     

OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS

The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form △(an△2(xn+bnxn-τ1+cnxn+τ2))+qnxβn+1-σ1+pnxβn+1+σ2=0,where{an},{bn},{cn},{qn}and{pn} are positive real sequences,β is a ratio of odd positive integers,τ1,τ2,σ1 and σ2 are positive integers.We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero.Some examples are presented to illustrate the main results.     

EXISTENCE OF NON-OSCILLATORY SOLUTIONS OF A CLASS OF HIGHER-ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH A FORCED TERM

In this paper, we consider a certain forced higher-order nonlinear neutral difference equation. By using Krasnoselskii's fixed point theorem and some new techniques, we obtain necessary and sufficient conditions for the existence of non-oscillatory solutions for the system. Our results extend the results of Zhang [5].     

具连续变量的中立型差分方程的振动性

本文研究如下具有连续变量的中立型差分方程△（y（t）-p（t）y（t-τ）） q（t）y（t-σ0=0,t≥to(*)其中q(t）∈C[to,∞）,R∧ ）,τ,σ是非负实数的解的振动性,获得了方程（*）的每个解都振动的若干充分条件,改进了文献中的结果。     

具有连续变量的差分方程的振动性

本文建立了具有连续变量的差分方程ｙ（ｔ）－ｐ（ｔ）ｙ（ｔ－τ）＋ｑ（ｔ）ｙ（ｔ－σ）＝０的振动性判据，这里ｐ（ｔ），ｑ（ｔ）∈Ｃ［［０，∞），Ｒ＋］，τ＞０，σ＞０     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，