期刊：
Journal of Applied Mathematics and Computing,2003年11(1-2):173-183 ISSN：1598-5865
通讯作者：
Li, X.
作者机构：
[Li, Xianyi] Department of Mathematics and Physics, Nanhua University, Hengyang, Human, P.R. China;[Zhou, Yong] Department of Mathematics, Xiangtan University, Xiangtan, Human, P.R. China
通讯机构：
Dept. of Mathematics and Physics, Nanhua University, China
关键词：
Classification;Existence of nonoscillatory solutions;Neutral difference equations
摘要：
In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form
$$\Delta ^2 (x_n - c_n x_{n - \tau } ) = f(n, x_{g_1 (n)} ,..., x_{g_m (n)} ).$$
Some existence results for each kind of nonoscillatory solutions are also established.
作者机构：
[Li, XY] School of Mathematics and Physics, Nanhua University, Hengyang 421001, China;[Li, XY; Zhu, DM] Department of Mathematics, East China Normal University, Shanghai 200062, China
通讯机构：
[Li, XY ] ;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.
关键词：
positive and negative coefficients;neutral differential equation;oscillation;eventually positive solution
摘要：
New sufficient conditions for the oscillation are obtained for all solutions of a class of first order neutral differential equations with positive and negative coefficients.
期刊：
Journal of Difference Equations and Applications,2003年9(9):833-839 ISSN：1023-6198
通讯作者：
Li, XY
作者机构：
[Li, XY] Nanhua Univ, Dept Math & Phys, Hengyang 421001, Peoples R China.;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.
通讯机构：
[Li, XY] N;Nanhua Univ, Dept Math & Phys, Hengyang 421001, Peoples R China.
关键词：
rational difference equation;global asymptotic stability;semicycle;equilibrium point
摘要：
In this paper, a sufficient condition is obtained for the global asymptotic stability of the following rational difference equation x(n+1) = x(n)x(n-1)+a/x(n)+x(n-1), n = 0, 1, 2,..., where a is an element of [0, infinity) and the initial values x(-1), x(0) is an element of (0, infinity).
摘要：
Oscillation properties of the solutions of a class of odd order neutral delay parabolic differential equations were investigated via the method of differential inequalities. Necessary and sufficient conditions for oscillation of odd order neutral delay parabolic differential equations were studied. Numerical method were used for the investigation .
作者机构：
Nanhua Univ, Dept Math & Phys, Henyang 421001, Peoples R China.;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.;[Ruan Hang; Zhang Lei; Long Teng] Beijing Institute of Technology
通讯机构：
Department of Mathematics and Physics, Nanhua University, China
关键词：
Population model;oscillation;convergence;permanence
摘要：
In this paper, the qualitative behavior of solutions of the bobwhite quail population model x(n+1) = ax(n) + bx(n)/(1 x(n-k)(p))(c), n = 0, 1, ..., where 0 < a < 1 < a + b, p, c is an element of (0, infinity) and k is a nonnegative integer, is investigated. Some necessary and sufficient as well as sufficient conditions for all solutions of the model to oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions axe derived. Furthermore, the permanence of every positive solution of the model is also showed. Many known results axe improved and extended and some new results are obtained for G. Ladas' open problems.
摘要：
Several comparison theorems for oscillation and nonoscillation of neutral difference equations with continuous arguments are established. Some known results are included and improved. All results obtained in this paper are new.
