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We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not eventually equal to one. 相似文献
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In this paper, we consider geometric aspects of a rational, planar system of difference equations defined on the open first quadrant and whose behaviour is governed by four independent, non-negative parameters. This system, indexed as (23, 23) in the notation of Ladas (Open problems and conjectures, J. Differential Equ. Appl. 15(3) 2009, pp. 303–323), is one of the 200 systems from Ladas about which little is known. Using geometric techniques, we answer several questions concerning the behaviour of this system. 相似文献
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Motivated by ideas from papers: C. Cinar, I. Yalçinkaya, S. Stević, A note on global asymptotic stability of a family of rational equations, Rostock. Math. Kolloq. 59 (2004), 41–49, and S. Stević, Global stability and asymptotics of some classes of rational difference equations, J. Math. Anal. Appl. 316 (2006), 60–68, here we confirm a conjecture on a rational symmetric difference equation from the paper: K. Berenhaut, J. Foley, S. Stević, The global attractivity of the rational difference equation , Appl. Math. Lett. 20 (2007), 54–58. 相似文献
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Xianyi Li 《Journal of Mathematical Analysis and Applications》2005,311(1):103-111
In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation:
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G. Martelli 《Journal of Difference Equations and Applications》2013,19(3):327-331
The explicit solution of four-point linear partial difference equations, provided with variable coefficients and with boundary conditions including the independent variables, was found in a previous note. In addition, the note explained the procedure to be used in case of boundary conditions also including the dependent variables. The aim of this note is to determine the explicit solution of a three-point equation of the above-mentioned second type, encountered in the study of differential difference equations with the method of the steps. 相似文献
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Kenneth S. Berenhaut Stevo Stevi? 《Journal of Mathematical Analysis and Applications》2007,326(2):940-944
This paper studies global asymptotic stability for positive solutions to the equation
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Xianyi Li 《Journal of Mathematical Analysis and Applications》2005,312(2):555-563
In this paper, we use a method different from the known literature to investigate the global behavior of the following fourth-order rational difference equation:
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Xianyi Li 《Journal of Mathematical Analysis and Applications》2007,334(1):528-533
By making use of inclusion theorem, we show in this paper the existence of solutions with a single semicycle for a general second-order rational difference equation. As a corollary, our results positively confirm Conjectures 4.8.3 and 5.4.6 in [M.R.S. Kulenovic, G. Ladas, Dynamics of Second-Order Rational Difference Equations, with Open Problems and Conjectures, Chapman and Hall/CRC, 2002]. 相似文献
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With the generalized bilinear operators based on a prime number , a Hirota-Satsuma-like equation is proposed. Rational solutions are generated and graphically described by using symbolic computation software Maple. 相似文献
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周英告 《高校应用数学学报(英文版)》2003,18(1):53-58
§ 1 IntroductionConsiderthenonautonomousdelaylogisticdifferenceequationΔyn =pnyn( 1 - yτ(n) ) ,n =0 ,1 ,2 ,...,( 1 1 )wherepn ∞n =0 isasequenceofpositiverealnumbers ,τ(n) ∞n =0 isanondecreasingsequenceofintegers,τ(n) <nandlimn→∞τ(n) =∞ ,Δyn=yn +1- yn.Motivatedbyplausibleapplications… 相似文献