On the Difference Equation xn+1=xnxn-k/(xn-k+1a+bxnxn-k) by Stevo Stević, Josef Diblík, Bratislav Iričanin, Zdenĕk Šmarda

“…We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ are real numbers, can be solved in closed form considerably extending the results in the literature. …”
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Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme by Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh, Getachew Adamu Derese

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On the Recursive Sequence x(n+!) = x(n-14) / [1 + x(n-2) x(n-5) x(n-8) x(n-11)] by Dağistan Şimşek, Burak Oğul

Subjects: “…difference equations…”
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On some new N-independent-variable discrete inequalities of the Gronwall type by En Hao Yang

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A Study of Nonlinear Fractional q-Difference Equations with Nonlocal Integral Boundary Conditions by Ahmed Alsaedi, Bashir Ahmad, Hana Al-Hutami

“…This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional q-difference equations with nonlocal integral boundary conditions. …”
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Dynamics of positive solutions of a three dimensional higher order system of difference equations by Murad Khan Hassani, Yasin Yazlik, Nouressadat Touafek

“…In this paper, we study the global behavior of positive solutions of the following system of difference equations xn+1=A+ynyn−k,yn+1=A+znzn−k,zn+1=A+xnxn−k,n∈ℕ0,A>0x−i,y−i,z−i,i∈{0,1,2,…,k}k∈ℕ…”
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Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order by Guangwang Su, Taixiang Sun, Bin Qin

“…We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). …”
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Dynamical Behavior and Expressions of Solutions of a Class of Higher-Order Nonlinear Difference Equations by Ghada AlNemer, Lama Sh. Aljoufi, A. M. Ahmed, Samir Al Mohammady, M. Zakarya, H. M. Rezk

“…The aim of this article is to get the forms of the solutions of the following nonlinear higher-order difference equations χs+1=χs−3k+1/±1±Πl=1kχs−3l+1,s=0,1,2,…, where the initial conditions χ−j,j=0,1,2,…,3k−1 and k∈1,2,… are arbitrary real numbers. …”
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Dynamics of a general model of nonlinear difference equations and its applications to LPA model by Wedad Albalawi, Fatemah Mofarreh, Osama Moaaz

Subjects: “…difference equations…”
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Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations by Mohamed S. Mohamed, Khaled A. Gepreel, Faisal A. Al-Malki, Nouf Altalhi

“…A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. …”
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Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator by Ruyun Ma, Yanqiong Lu

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The Asymptotic Behavior of Solutions for a Class of Nonlinear Fractional Difference Equations with Damping Term by Zhihong Bai, Run Xu

“…Based on generalized Riccati transformation and some inequalities, some oscillation results are established for a class of nonlinear fractional difference equations with damping term. An example is given to illustrate the validity of the established results.…”
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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

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Global Behavior of the Max-Type Difference Equation xn+1=max⁡{1/xn,An/xn−1} by Taixiang Sun, Bin Qin, Hongjian Xi, Caihong Han

“…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≤inf⁡An≤sup⁡An<1. …”
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A proton therapy model using discrete difference equations with an example of treating hepatocellular carcinoma by Erin N. Bodine, K. Lars Monia

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Anticontrol of Chaos for a Class of Delay Difference Equations Based on Heteroclinic Cycles Connecting Repellers by Zongcheng Li

“…This paper is concerned with anticontrol of chaos for a class of delay difference equations via the feedback control technique. …”
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Sequential Derivatives of Nonlinear q-Difference Equations with Three-Point q-Integral Boundary Conditions by Nittaya Pongarm, Suphawat Asawasamrit, Jessada Tariboon

“…This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear q-difference equations with three-point q-integral boundary conditions. …”
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Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations by Susan D. Lauer, Johnny Henderson

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Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations by Raafat Abo-Zeid, Abdul Qadeer Khan

“…In this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. …”
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A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation by Xi-Xiang Xu, Meng Xu

“…An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. …”
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