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In this note, we investigate the periodic character of solutions of the nonlinear, second-order difference equation
where the parameter A and the initial conditions x0 and x1 are positive real numbers. We give sufficient conditions under which every positive solution of this equation converges to a period two solution.  相似文献   

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Under the framework of uniformly smooth Banach spaces, Chang[1] proved in 2006 that the sequence {xn} generated by the iteration xn+1 = αn+1f(xn) + (1 - αn+1)Tn+1xn converges strongly to a common fixed point of a finite family of nonexpansive maps {Tn}, where f : C → C is a contraction. However, in this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping.  相似文献   

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我们研究差分方程(1)的解的渐近性和全局吸引性.  相似文献   

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Our goal in this article is to complete the study of the behavior of solutions of the equation in the title when the parameter p is positive and the initial conditions are arbitrary positive numbers. Our main focus is the case 0 < p < 1. We will show that in this case, all solutions which do not monotonically converge to the equilibrium have a subsequence which converges to p and a subsequence which diverges to infinity. For the sake of completeness, we will also present the results (which were previously known) with alternative proofs for the case p = 1 and the case p > 1.  相似文献   

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In this paper, we investigate the global behavior of the recursive sequencexn+1=α-βxnγ+g(xn-k)forn=0,1,,where α,β,γ0 and g(x) is a continuous function defined on (-,), which satisfies some additional conditions.  相似文献   

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We present some comments on the behavior of solutions of the difference equation where p i 0, i = 1,..., k, k N, and x k ,..., x –1 R.  相似文献   

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1 问题的提出我们经常遇到下列问题 :(1)已知 x,y∈ R ,且 x y =1,求 1x 4y 的最小值 ;(2 )已知 x,y∈ R ,且 x y =1,求 1x2 8y2 的最小值 ;问题 (1)“用 1代换”不难求得 :1x 4y =(1x 4y) (x y)   =5 yx 4 xy ≥ 5 2 yx .4 xy =9,当且仅当 yx =4 xy,即  y =2 x时取等号 .问题 (2 )能否“用 1代换”呢 ?1x2 8y2 =(1x2 8y2 ) (x y) ,  =1x 8y yx2 8xy2 ,虽然有  1x 8y ≥ 2 8xy ,yx2 8xy2 ≥ 2 8xy 且  1xy≥ 2x y,但三式等号分别在 y =8x,y =2 x与 y =x时成立 ,故等号不能同时成立 .在 (1x…  相似文献   

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从特殊情况研究多项式f(x)=x<'n>+1在有理域Q[x]上的因式分解情况.可以证明:f(x)不可约的充要条件是存在自然数q,使得n=2<'q>;多项式f(x)的因式数不小于n的奇子数加1,即D(f)≥H(n)+1;如果n是素数,那么D(f)=H(n)+1.  相似文献   

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差分方程xn+1=xanern(1-xn-k)正解的渐近性   总被引:2,自引:0,他引:2  
刘玉记 《经济数学》2000,17(3):66-74
本文研究时滞Logistic方程 xn+1=xanern(1-xn-k),n=0,1,2,… (*) 其中rn是非负实数列,a∈(0,1],k为非负整数,获得了保证方程(*)的每一正解趋于1的一些充分条件,推广和改进了文[1]的结果.  相似文献   

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从特殊情况研究多项式f(x)=x<'n>+1在有理域Q[x]上的因式分解情况.可以证明:f(x)不可约的充要条件是存在自然数q,使得n=2<'q>;多项式f(x)的因式数不小于n的奇子数加1,即D(f)≥H(n)+1;如果n是素数,那么D(f)=H(n)+1.  相似文献   

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