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OSCILLATION THEOREMS FOR A NEUTRAL delay difference equation

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Annals of Differential equations 1997年第4期13卷 377-384页

作者：罗交晚长沙铁道学院 410075

Consider the neutral delay difference equation △[p(t)x(t)-q(t)x(t-τ)] + r(t)x(t-δ(t)) =0 (*)where t ∈{a, a + 1, a + 2,…} and p(t) > 0, q(t) ≥ 0, r(t) ≥ 0, δ(t) ∈ {0, 1, 2,…} with,lim(t-δ(t)) =∞ and τ∈ { 1, 2, 3,…}. Note that the delay of the difference equation may vary, thus the equation may not be of constant order. We obtain some sufficient conditions for the oscillation of equation (*) and the second order self-adjoint difference equation △[p(t-1)△y(t-1)]+r(t)y(t) = *** the work in Timothy Peil [5] is *** (1991) No. 39A10, 39A12

关键词： delay difference equation oscillation self-adjoint

Linearized Oscillations in Nonlinear delay difference equations

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Acta Mathematica Sinica,English Series 1999年第4期15卷 569-574页

作者： Sanyi Tang Department of Computer and Mathematics,Hubei Institute for Nationalities,Enshi 445000,P.R.ChinaYanni Xiao Institute of Mathematics,Academia Sinica,Beijing 100080,P.R.China E-mail:xyn@math03.math.ac.cnJufang Chen Department of Mathematics,Shanxi Normal University,Xi’an 710062,P.R.China Department of Computer and Mathematics Hubei Institute for Nationalities Enshi P. R. China Institute of Mathematics Academia Sinica Beijing P. R. China Department of Mathematics Shanxi Normal University Xi’an P. R. China

Consider the nonlinear delay difference equation xn+1-xn+sum j=1 to m pjfj（xn-kj）=0. We establish a linearized oscillation result of this equation,which is the extension of the result in the paper [1].

关键词： delay difference equation Oscillatory Nonoscillatory

BOUNDEDNESS AND PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY FOR A CLASS OF delay difference equationS WITH HIGHER ORDER

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Applied Mathematics and Mechanics(English Edition) 2002年第11期23卷 1331-1338页

作者：李先义 Department of Mathematics and Physics Nanhua UniversityHengyangHunan 421001P R China Department of Mathematics East China Normal UniversityShanghai 200062P R China

Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open ... 详细信息

关键词： delay difference equation boundedness and persistence global asymptotic stability open problem

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARdelay difference equationS

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Applied Mathematics and Mechanics(English Edition) 2002年第3期23卷 355-362页

作者： LIU Yu-ji(刘玉记) Department of Mathematics Yueyang Teachers'' College Yueyang 414000 P R China

The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was discussed. The sufficient conditions that guarantee every solution to converge to zero are obtained. Many known results are improved and generated.

关键词： global attractivity nonlinear nonautonomous delay difference equation

Oscillation of High Order Neutral delay difference equations with Continuous Arguments

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Journal of Mathematical Research and Exposition 2010年第2期30卷 374-380页

作者： Mei HUANG Jian Hua SHEN Department of Mathematics and Physics Hunan First Normal College Hunan 410002 P. R. China College of Mathematics and Computer Science Hunan Normal University Hunan 410081 P. R. China

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... 详细信息

关键词： delay difference equation bounded solution oscillation nonoscillation.

Global Attractivity of a Kind of delay difference equations

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Chinese Quarterly Journal of Mathematics 2002年第1期17卷 9-18页

作者：李先义朱德明金银来南华大学数理部湖南衡阳421001 华东师范大学数学系上海200062 临沂师范学院数学系山东临沂276005

Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture fo... 详细信息

关键词： delay difference equation global attractivity positive semicycle negative semicycle periodic point of prime period two

ASYMPTOTIC STABILITY OF THIRD ORDER delay difference equationS WITH THREE PARAMETERS

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Annals of Differential equations 2009年第4期25卷 453-465页

作者： Yantao Wang, Hongshan Ren (Institute of Math. Science, Heilongjiang University, Harbin 150080 )

In this paper, we obtain a necessary and sufficient condition for the asymptotical stability of the zero solution to the third order delay difference equations.

关键词： delay difference equation asymptotic stability characteristic equation

MULTIPLE POSITIVE PERIODIC SOLUTIONS OF A CLASS OF delay difference equationS

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Annals of Differential equations 2006年第3期22卷 299-303页

作者： Kang Shugui Liu Xilan Shi Bao ( Institute of Applied Math., Naval Aeronautical Engineering Institute, Yantai 264001 Dept. of Math., Yanbei Normal University, Datong 037009)

Based on the Leggett-Williams fixed point theorem for a Banach space, we establish the existence of three positive periodic solutions for a class of delay difference equations.

关键词： delay difference equation periodic positive solution cone fixed point theorem

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A CONJECTURE BY ***

Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 39-44页

作者： LIXIANYI TANGHENGSHENG LIUYACHUN XIAOGONGFU BasicSeiencesDepartment Central-SouthInstituteofTechnologyHengyangt421001. BasicSciencesDepartment HengyangBranchofHunanUniversityHengyang421001.

In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by *** is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1, x0∈(0,∞). Received June 2,1997. Revised September 15, 1997.1991 MR Subject Classification:39A10.

关键词： delay difference equation boundedness and persistence.