共查询到20条相似文献,搜索用时 0 毫秒
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We investigate the global character of solutions of the equation in the title with positive parameters and positive initial conditions. We obtain results about the global attractivity of the equilibrium, the existence and attractivity of the period-two solution and the semicycles. 相似文献
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We investigate the boundedness nature of positive solutions of the difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\},n = 0,1,..., $$ where {A n } n=0 ∞ and {B n } n=0 ∞ are periodic sequences of positive real numbers. 相似文献
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Stevo Stević 《Journal of Applied Mathematics and Computing》2005,18(1-2):229-234
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}, n = 0,1,...$$ is investigated, where all the coefficients are nonnegative real numbers. 相似文献
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Marwan Aloqeili 《Journal of Applied Mathematics and Computing》2007,25(1-2):375-382
We study, firstly, the dynamics of the difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - 1}^p }}$ , withp ∈ (0,1) and α∈ [0, ∞). Then, we generalize our results to the (k + 1)th order difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - k}^p }}$ ,k = 2, 3,... with positive initial conditions. 相似文献
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The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n + 1} = \frac{{\alpha x_n + \beta x_{n - 1} + \gamma x_{n - 2} + \delta x_{n - 3} }}{{Ax_n + Bx_{n - 1} + Cx_{n - 2} + Dx_{n - 3} }},n = 0,1,2.....$ where the coefficientsA, B, C, D, α, β, γ, δ, and the initial conditionsx -3,x -2,x -1,x 0 are arbitrary positive real numbers. 相似文献
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In this paper we consider the difference equation $$x_{n + 1} = \frac{{a + bx_{n - k} - cx_{n - m} }}{{1 + g(x_{n - 1} )}},$$ wherea, b, c are nonegative real numbers,k, l, m are nonnegative integers andg(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation. 相似文献
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I. Baoulina 《Acta Appl Math》2005,85(1-3):35-39
We obtain an explicit formula for the number of solutions of a special equation in a finite field under a certain restriction on the exponents.
Mathematics Subject Classifications (2000) primary: 11G25, secondary: 11T24. 相似文献
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Stevo Stević 《Journal of Applied Mathematics and Computing》2006,21(1-2):223-232
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation $$x_{n + 1} = \frac{{ax_{n - 2m + 1}^p }}{{b + cx_{n - 2k}^{p - 1} }}, n = 0, 1,...$$ wherem, k ∈ N, 2k > 2m?1,a, b, c are nonnegative real numbers andp < 1, are investigated. 相似文献
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We investigate the existence of unbounded solutions and the period-two convergence of solutions of the equation in the title with the parameter γ positive, the remaining parameters nonnegative, and with nonnegative initial conditions. 相似文献
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V. P. Maslov 《Functional Analysis and Its Applications》1994,28(1):33-41
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The integral $$\int_0^{{\pi \mathord{\left/ {\vphantom {\pi 4}} \right. \kern-\nulldelimiterspace} 4}} {\ln \left( {\cos ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta \pm \sin ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta } \right)d\theta } $$ where m and n are relatively prime positive integers, is evaluated exactly in terms of elementary functions and the Catalan constant G. 相似文献
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E.A. Grove G. Ladas M. Predescu M. Radin 《Journal of Difference Equations and Applications》2013,19(2):171-199
We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x n +1 = f + n x n m (2 k +1) + i x n m 2 l A + x n m 2 l , n =0,1,… where k and l are non-negative integers, the parameters f , n , i , A are non-negative real numbers with f + n + i >0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters n , i and A . 相似文献
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Jian Hua Chen 《数学学报(英文版)》2002,18(4):765-778
In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family
of isometric immersions from M
n
1(c
1) ×M
n
2(c
2) to space forms M
n
(c) by introducing 2-parameter loop algebra.
Received July 14, 1999, Accepted June 15, 2000 相似文献
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Erd?s and Selfridge [3] proved that a product of consecutive integers can never be a perfect power. That is, the equation x(x?+?1)(x?+?2)...(x?+?(m???1))?=?y n has no solutions in positive integers x,m,n where m, n?>?1 and y?∈?Q. We consider the equation $$ (x-a_1)(x-a_2) \ldots (x-a_k) + r = y^n $$ where 0?≤?a 1?<?a 2?<???<?a k are integers and, with r?∈?Q, n?≥?3 and we prove a finiteness theorem for the number of solutions x in Z, y in Q. Following that, we show that, more interestingly, for every nonzero integer n?>?2 and for any nonzero integer r which is not a perfect n-th power for which the equation admits solutions, k is bounded by an effective bound. 相似文献