共查询到20条相似文献,搜索用时 78 毫秒
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We investigate the global stability, the periodic character and the boundedness nature of solutions of the equation in the title for all admissible nonnegative values of the parameters and the initial conditions. We show that the solutions exhibit a trichotomy character depending on how the parameter γ compares to the sum of the parameters δ and A. 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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H. M. El-Owaidy A. M. Ahmed Z. Elsady 《Journal of Applied Mathematics and Computing》2004,16(1-2):243-249
Our aim in this paper is to investigate the global attractivity of the recursive sequence $$x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }},$$ where α, β, γ >0 andk=1,2,… We show that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients. 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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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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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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In this paper, we solve the simultaneous Diophantine equations \(m \cdot ( x_{1}^k+ x_{2}^k +\cdots + x_{t_1}^k)=n \cdot (y_{1}^k+ y_{2}^k +\cdots + y_{t_2}^k )\), \(k=1,3\), where \( t_1, t_2\ge 3\), and m, n are fixed arbitrary and relatively prime positive integers. This is done by choosing two appropriate trivial parametric solutions and obtaining infinitely many nontrivial parametric solutions. Also we work out some examples, in particular the Diophantine systems of \(A^k+B^k+C^k=D^k+E^k\), \(k=1,3\). 相似文献
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John Mcleod 《Geometriae Dedicata》2011,152(1):1-16
We determine the maximal hyperbolic reflection groups associated to the quadratic forms ${-3x_0^2 + x_1^2 + \cdots + x_n^2, n \ge 2}$ , and present the Coxeter schemes of their fundamental polyhedra. These groups exist in dimensions up to 13, and a proof is given that in higher dimensions these quadratic forms are not reflective. 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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Hai Q. Dinh Abhay Kumar Singh Sukhamoy Pattanayak Songsak Sriboonchitta 《Designs, Codes and Cryptography》2018,86(7):1451-1467
We study the structure of cyclic DNA codes of odd length over the finite commutative ring \(R=\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2 + v^2\mathbb {F}_2+uv^2\mathbb {F}_2,~u^2=0, v^3=v\), which plays an important role in genetics, bioengineering and DNA computing. A direct link between the elements of the ring R and 64 codons used in the amino acids of living organisms is established by introducing a Gray map from R to \(R_1=\mathbb {F}_2+u\mathbb {F}_2 ~(u^2=0)\). The reversible and the reversible-complement codes over R are investigated. We also discuss the binary image of the cyclic DNA codes over R. Among others, some examples of DNA codes obtained via Gray map are provided. 相似文献
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Taixiang Sun Xin Wu Qiuli He Hongjian Xi 《Journal of Applied Mathematics and Computing》2014,44(1-2):61-68
In this paper, we study the difference equation $$x_{n+1}=p+\frac{x_{n-1}}{x_n}, \quad n=0,1,\ldots, $$ where initial values x ?1,x 0∈(0,+∞) and 0<p<1, and obtain the set of all initial values (x ?1,x 0)∈(0,+∞)×(0,+∞) such that the positive solutions $\{x_{n}\}_{n=-1}^{\infty}$ are bounded. This answers the Open problem 4.8.11 proposed by Kulenovic and Ladas (Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, 2002). 相似文献
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In this paper, we investigate the global asymptotic stability, the periodicity nature and the boundedness character of the positive solutions of the difference equation x n+1=(α+β x n?k )/(γ?x n ) where n=0,1,2,… and k∈{1,2,…}. The parameters α≥0, γ,β>0 and the initial conditions x ?k , x ?k+1,…,x ?1,x 0 are real positive numbers. We show that the positive equilibrium point of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients α,β,γ. 相似文献
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ChaoHua Jia 《中国科学 数学(英文版)》2012,55(3):465-474
If n is a positive integer,let f (n) denote the number of positive integer solutions (n 1,n 2,n 3) of the Diophantine equation 4/n=1/n1 + 1/n2 + 1/n3.For the prime number p,f (p) can be split into f 1 (p) + f 2 (p),where f i (p) (i=1,2) counts those solutions with exactly i of denominators n 1,n 2,n 3 divisible by p.In this paper,we shall study the estimate for mean values ∑ p相似文献