Global Attractivity of a Family of Max-Type Difference Equations by Xiaofan Yang, Wanping Liu, Jiming Liu

“…We propose to study a generalized family of max-type difference equations and then prove the global attractivity of a particular case of it under some parameter conditions. …”
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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations by Jan Čermák, Tomáš Kisela, Luděk Nechvátal

“…We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. …”
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Recent Trends in Computational and Theoretical Aspects in Differential and Difference Equations by Ram Jiwari, Mehmet Emir Koksal, Haydar Akca

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Symmetries, Associated First Integrals, and Double Reduction of Difference Equations by L. Ndlovu, M. Folly-Gbetoula, A. H. Kara, A. Love

“…We determine the symmetry generators of some ordinary difference equations and proceeded to find the first integral and reduce the order of the difference equations. …”
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On the Solutions of a System of Third-Order Rational Difference Equations by A. M. Alotaibi, M. S. M. Noorani, M. A. El-Moneam

“…The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2), yn+1=xnxn-2/(±yn-1±xn-2), n=0,1,…, is clarified in which the initial conditions x-2, x-1, x0, y-2, y-1, y0 are considered as arbitrary positive real numbers. …”
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Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation by Wen-Xiu Ma

“…We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c),  n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.…”
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On a Class of Discrete Max-Type Difference Equation Model of Order Four by A. M. Alotaibi, Abdul Khaliq, Muhammad Ali, Stephen Sadiq

“…The global dynamical behavior of a class of discrete models known as the max-type difference equation model is the subject of the research. …”
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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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Global attractivity of a higher order nonlinear difference equation with decreasing terms by Xiao Wang, Chuanxi Qian

Subjects: “…higher order nonlinear difference equation…”
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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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Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces by Rigoberto Medina

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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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