Global attractivity of a rational difference equation with higher order and its applications by Xianyi Li, Luyao Lv

Subjects: “…rational difference equation with higher order…”
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A Comparison Theorem for Oscillation of the Even-Order Nonlinear Neutral Difference Equation by Quanxin Zhang

“…A comparison theorem on oscillation behavior is firstly established for a class of even-order nonlinear neutral delay difference equations. By using the obtained comparison theorem, two oscillation criteria are derived for the class of even-order nonlinear neutral delay difference equations. …”
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Global Behavior of the Difference Equation xn+1=xn-1g(xn) by Hongjian Xi, Taixiang Sun, Bin Qin, Hui Wu

“…We consider the following difference equation xn+1=xn-1g(xn), n=0,1,…, where initial values x-1,x0∈[0,+∞) and g:[0,+∞)→(0,1] is a strictly decreasing continuous surjective function. …”
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On the Difference Equation xn=anxn-k/(bn+cnxn-1⋯xn-k) by Stevo Stević, Josef Diblík, Bratislav Iričanin, Zdeněk Šmarda

“…The behavior of well-defined solutions of the difference equation xn=anxn-k/(bn+cnxn-1⋯xn-k), n∈ℕ0, where k∈ℕ is fixed, the sequences an, bn and cn are real, (bn,cn)≠(0,0), n∈ℕ0, and the initial values x-k,…,x-1 are real numbers, is described.…”
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Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation by Zhiping Liu, Shugui Kang, Huiqin Chen, Jianmin Guo, Yaqiong Cui, Caixia Guo

“…We investigate the existence of solutions for a Caputo fractional difference equation boundary value problem. We use Schauder fixed point theorem to deduce the existence of solutions. …”
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Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers by Li He, Wanping Liu

“…This paper studies a third-order conditional difference equation which is a generalization from the literature. …”
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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation by M. E. Erdogan

“…The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. …”
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Global Dynamics of Some 3 × 6 Systems of Exponential Difference Equations by A. Q. Khan, A. Sharif

“…We study the global dynamics of a list of following 3×6 systems of exponential difference equations: xn+1=α4+β4e-yn/γ4+yn-1, yn+1=α5+β5e-zn/γ5+zn-1, zn+1=α6+β6e-xn/γ6+xn-1, xn+1=α7+β7e-zn/γ7+zn-1, yn+1=α8+β8e-xn/γ8+xn-1, zn+1=α9+β9e-yn/γ9+yn-1, xn+1=α10+β10e-xn/γ10+xn-1, yn+1=α11+β11e-yn/γ11+zn-1, zn+1=α12+β12e-zn/γ12+yn-1, xn+1=α13+β13e-xn/γ13+zn-1, yn+1=α14+β14e-yn/γ14+yn-1, zn+1=α15+β15e-zn/γ15+xn-1, xn+1=α16+β16e-xn/γ16+yn-1, yn+1=α17+β17e-yn/γ17+xn-1,  zn+1=α18+β18e-zn/γ18+zn-1, where αi,βi,γi,i=4,5,⋯,18 and the initial conditions x0,x-1,y0,y-1,z0,z-1 are arbitrary nonnegative real numbers. …”
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Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations by Zhinan Xia

“…We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. …”
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New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces by Rigoberto Medina

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Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations by Habtamu Garoma Debela, Solomon Bati Kejela, Ayana Deressa Negassa

“…This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. …”
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Impulsive Antiperiodic Boundary Value Problems for Nonlinear qk-Difference Equations by Lihong Zhang, Bashir Ahmad, Guotao Wang

“…We show the existence and uniqueness of solutions for an antiperiodic boundary value problem of nonlinear impulsive qk-difference equations by applying some well-known fixed point theorems. …”
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Global Character of a Six-Dimensional Nonlinear System of Difference Equations by Mehmet Gümüş, Yüksel Soykan

“…The aim of this paper is to study the dynamical behavior of positive solutions for a system of rational difference equations of the following form: un+1=αun-1/β+γvn-2p, vn+1=α1vn-1/β1+γ1un-2p, n=0,1,…, where the parameters α,β,γ,α1,β1,γ1,p and the initial values u-i,v-i for i=0,1,2 are positive real numbers.…”
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On Nonlinear Boundary Value Problems for Functional Difference Equations with p-Laplacian by Yong Wan, Yuji Liu

“…Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations with p-Laplacian are established by making of continuation theorems. …”
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A Group Theory Approach towards Some Rational Difference Equations by Mensah Folly-Gbetoula, Nkosingiphile Mnguni, A. H. Kara

“…A full Lie point symmetry analysis of rational difference equations is performed. Nontrivial symmetries are derived, and exact solutions using these symmetries are obtained.…”
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On the Global Asymptotic Stability of a Second-Order System of Difference Equations by Ibrahim Yalcinkaya

“…A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations 𝑧𝑛+1=(𝑡𝑛𝑧𝑛−1+𝑎)/(𝑡𝑛+𝑧𝑛−1),𝑡𝑛+1=(𝑧𝑛𝑡𝑛−1+𝑎)/(𝑧𝑛+𝑡𝑛−1),𝑛=0,1,2,…, where the parameter 𝑎𝜖(0,∞) and the initial values (𝑧𝑘,𝑡𝑘)𝜖(0,∞) (for 𝑘=−1,0).…”
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Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations by Allaberen Ashyralyev, Okan Gercek

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Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type by Janusz Migda, Małgorzata Migda, Magdalena Nockowska-Rosiak

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Uniqueness and Existence of Solution for a System of Fractional q-Difference Equations by Wen-Xue Zhou, Hai-zhong Liu

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Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales by Tongxing Li, Josef Diblík, Alexander Domoshnitsky, Yuriy V. Rogovchenko, Felix Sadyrbaev, Qi-Ru Wang

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