OSCILLATION AND EXISTENCE OF POSITIVESOLUTIONS OF DIFFERENTIAL EQUATIONSWITH POSITIVE, NEGATIVE COEFFICIENTS

This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The "sharp" conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.     

一类非线性差分方程正解的不存在性

本文研究一类非线性差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了[1]的结果。     

OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS

We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and     

一类二阶中立型时滞差分方程解的振动性

研究了二阶中立型时滞差分方程Δ(an(Δ(xn+pnxn-τ))α)+qnxnβ-σ=0解的振动性的几个充分条件,改进和推广了文献中的有关结论。     

具有连续变量的中立型差分方程解的振动性

本获得了具有连续变量的中立型差分方程Δ[x(t)-p(t)x(t-τ)] q(t)f(x(t-σ)=0的所有解振动的几个充分条件。     

具有可变时滞的偶数阶非线性中立型差分方程的正解

本文考虑具有可变时滞的偶数阶非线性中立型差分方程，利用Ｂａｎａｃｈ空间的压缩映象原理，得到了这类方程存在最终正解的判别准则．     

Non-wandering sets of the powers of dendrite maps

Let(X, d) be a metric space and f be a continuous map from X to X. Denote by EP(f)and Ω(f) the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree map f, the following statements hold:(1) If x ∈Ω(f)-Ω(f~n) for some n ≥ 2,then x ∈ EP(f).(2) Ω(f) is contained in the closure of EP(f). The aim of this note is to show that the above results do not hold for maps of dendrites D with Card(End(D)) = ?0(the cardinal number of the set of positive integers).     

On the solutions of a max‐type difference equation system

In this paper, we study behavior of the solution of the following max‐type difference equation system: where , the parameter A is positive real number, and the initial values x₀,y₀ are positive real numbers. Copyright © 2014 John Wiley & Sons, Ltd.     

高阶非线性差分方程的正解

本文讨论了一类奇数阶非线性中立型差分方程,获得了正解存在的充要条件和比较定理．     

拟正则半群的圈积嵌入与矩阵同余

给出了拟正则半群的圈积嵌入．研究了幂等元集 Ｅ Ｓ 生成的子半群〈 Ｅ Ｓ〉上的矩阵同余可扩张为 Ｓ上的矩阵同余的条件． 特别地,如果〈 Ｅ Ｓ〉上的最小矩阵同余可扩张为 Ｓ上的矩阵同余,那么〈 Ｅ Ｓ〉上的每个矩阵同余可扩张为 Ｓ上的矩阵同余