Global Behavior of the Max-Type Difference Equation xn+1 = max{1/xn, An/xn-1}

Taixiang Sun; Bin Qin; Hongjian Xi; Caihong Han
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
We study global behavior of the following max-type difference equation xn+1 = max(1/xn,An/xn-1), n = 0, 1, . . . , where (An)∞n=0 is a sequence of positive real numbers with 0 = infAn = supAn < 1. The special case when (An)∞n=0 is a periodic sequence with period k and An ∈ (0, 1) for every n ≥ 0 has been completely investigated by Y. Chen. Here we extend his results to the general case.


Related Articles

  • Behavior of a rational recursive sequences. Mohamed Elsayed, Elsayed M. // Studia Universitatis Babes-Bolyai, Mathematica;2011, Vol. 56 Issue 1, p27 

    We obtain in this paper the solutions of the difference equations xn+1 = xn-7/±1 ± xn-1xn-3xn-5xn-7, n = 0, 1, …, where the initial conditions are arbitrary nonzero real numbers.

  • Oscillation of Neutral Advanced Difference Equation. Murugesan, A. // Global Journal of Pure & Applied Mathematics;2013, Vol. 9 Issue 1, p45 

    In this article, we establish oscillation criteria for solutions to the first order neutral advanced difference equation Δ[x(n) - p(n)x(τ(n))] - q(n)x(σ(n)) = 0, n ≥ n0 (*) where {p(n)}, {q(n)} are sequences of real numbers, {σ(n)} is a sequence of positive integers such that...

  • Dynamics and behavior of a higher order rational difference equation. Elsayed, E. M. // Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 4, p1464 

    We study the global result, boundedness, and periodicity of solutions of the difference equation xn+1 = a bxn-1 + cxn-k/dxn-1 + exn-k, n = 0,1,..., where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x -t, x - t+1, . . ., x -1 and x0 are positive real...

  • A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n) = -p(n)x(n - k) with a Positive Coefficient. Baštinec, J.; Berezansky, L.; Diblík, J.; Šmarda, Z. // Abstract & Applied Analysis;2011, Special section p1 

    A linear (k + 1)th-order discrete delayed equation Δx(n) = -p(n)x(n - k) where p(n) a positive sequence is considered for n → ∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite...

  • On the Dynamics of the Recursive Sequence. Zengın, Saime; Öztürk, İlhan; Bozkurt, Fatma // Gazi University Journal of Science;Jan2010, Vol. 23 Issue 1, p53 

    Our aim in this paper is to investigate the local stability of the positive solutions of the difference equation (This equation cannot be represented in ASCII code value) where the initial conditions y-1, y0 are arbitrary positive real numbers such that yn ≠ 0 for n= -1,0,1,…, ,...

  • Solutions and Properties of Some Degenerate Systems of Difference Equations. Alzahrani, E. O.; El-Dessoky, M. M.; Elsayed, E. M.; Yang Kuang // Journal of Computational Analysis & Applications;Jan2015, Vol. 18 Issue 1, p321 

    This paper is devoted to obtain the form of the solution and the qualitative properties of the following systems of a rational difference equations of order two ... with positive initial conditions x-1, x0, y-1 and y0 are nonzero real numbers. If we let un = xnxn-1 and vn = ynyn-1, then these...

  • Some New Volterra-Fredholm-Type Discrete Inequalities and Their Applications in the Theory of Difference Equations. Bin Zheng; Qinghua Feng // Abstract & Applied Analysis;2011, Special section p1 

    Some new Volterra-Fredholm-type discrete inequalities in two independent variables are established, which provide a handy tool in the study of qualitative and quantitative properties of solutions of certain difference equations. The established results extend some known results in the literature.

  • Advanced Discrete Halanay-Type Inequalities: Stability of Difference Equations. Agarwal, Ravi P.; Young-Ho Kim; Sen, S. K. // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1 

    We derive new nonlinear discrete analogue of the continuous Halanay-type inequality. These inequalities can be used as basic tools in the study of the global asymptotic stability of the equilibrium of certain generalized difference equations.

  • Lyapunov-type inequalities for nonlinear impulsive systems with applications. Kayar, Zeynep; Zafer, Ağacık // Electronic Journal of Qualitative Theory of Differential Equatio;2016, Issue 1-122, p1 

    We obtain new Lyapunov-type inequalities for systems of nonlinear impulsive differential equations, special cases of which include the impulsive Emden-Fowler equations and half-linear equations. By applying these inequalities, sufficient conditions are derived for the disconjugacy of solutions...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics