共查询到20条相似文献,搜索用时 15 毫秒
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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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From previous studies of the equation in the title with positive parameters p and q and positive initial conditions we know that if q h 4 p + 1 then the equilibrium is a global attractor. We also know that if q > 4 p + 1 then every solution eventually enters and remains in the interval [ p / q , 1]. In this strip there exists a "unique" prime period two solution that is locally asymptotically stable. In this paper, we provide more insight as to the behavior of solutions of the equation in the title in the strip [ p / q , 1], where a one-dimensional stable manifold lives. 相似文献
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B.D. Mestel 《Journal of Difference Equations and Applications》2013,19(2):201-209
We study the second-order difference equation x n +1 = f ( x n ) x n m 1 where f ] C 1 ([0, X ),[0, X )) and x n ] (0, X ) for all n ] Z . For the cases p h 5, we find necessary and sufficient conditions on f for all solutions to be periodic with period p . We answer some questions and conjectures of Kulenovi ' and Ladas. 相似文献
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We investigate the boundedness character, the oscillatory and periodic nature and global attractivity of the nonnegative solutions of the difference equation where the parameters α and β are nonnegative real numbers and g(x) is a continuous function on [0, ∞), which satisfies some additional conditions. 相似文献
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The aim of this paper is to give an account of some results recently obtained in Combinatorial Dynamics and apply them to get for k S 2 the periodic structure of delayed difference equations of the form x n = f ( x n m k ) on I and S 1 . 相似文献
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J. Feuer 《Applicable analysis》2013,92(6):599-606
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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Guo Xiaoyan 《Periodica Mathematica Hungarica》2013,66(1):87-93
Let a, b be fixed positive integers such that a ≠ b, min(a, b) > 1, ν(a?1) and ν(b ? 1) have opposite parity, where ν(a ? 1) and ν(b ? 1) denote the highest powers of 2 dividing a ? 1 and b ? 1 respectively. In this paper, all positive integer solutions (x, n) of the equation (a n ? 1)(b n ? 1) = x 2 are determined. 相似文献
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In this note, we study the global existence of classical solutions for the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Based on the Schauder type estimates and energy estimates, we establish the global existence of classical solutions. 相似文献
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Xing-Xue Yan Wan-Tong Li Zhu Zhao 《Journal of Applied Mathematics and Computing》2005,17(1-2):269-282
We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n + 1} = \alpha - \frac{{x_n }}{{x_{n - 1} }}, n = 0,1,...,$$ where α∈R is a real number, and the initial conditionsx?1,x 0 are arbitrary real numbers. 相似文献
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In this study, we determine when the Diophantine equation x 2?kxy+y 2?2 n = 0 has an infinite number of positive integer solutions x and y for 0 ? n ? 10. Moreover, we give all positive integer solutions of the same equation for 0 ? n ? 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x 2 ? kxy + y 2 ? 2 n = 0. 相似文献
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Peter M. Knopf 《Journal of Difference Equations and Applications》2013,19(7):607-619
Consider the third-order difference equation x n+1 = (α+βx n +δx n ? 2)/(x n ? 1) with α ∈ [0,∞) and β,δ ∈ (0,∞). It is shown that this difference equation has unbounded solutions if and only if δ>β. 相似文献
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文[1]为证明2001年第42届IMO第2题而通过独特的思路给出了一个恒等式;设实数ai,bi∈R,A^3=n∑i=1ai^3,B^3=n∑i=1bi^3,且AB≠0,则有恒等式 相似文献
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胡舒合 《数理统计与应用概率》1994,9(1):76-83
设(dni,i=1,...n),(Xni,i=1,...,n)分别为双下标常数列和随机变量列,众所周知,有关n∑i=1dniXni的收敛性问题,在统计推断中有着广泛的应用,例如在异方差的回归分析中的重要应用(3),当(Xni,Fni,-∞<i<∞)为鞅差序列时,文献(4)研究了∑iXni的渐进正态性,本文获得n∑i=1dniXni的P阶均方收敛及强收敛于零的充分条件,其(Xni,i=1,...,n 相似文献
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