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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Existence and Nonexistence of Periodic Solutions for a Class of Fourth-Order Partial Difference Equations by Dan Li, Yuhua Long

“…In this paper, we investigate multiplicity, existence, and nonexistence of periodic solutions to a fourth-order partial difference equation via linking theorem and saddle point theorem. …”
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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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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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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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Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. …”
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Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation by Huiqin Chen, Shugui Kang, Lili Kong, Ying Gao

“…A class of boundary value problems of Caputo fractional q-difference equation is introduced. Green’s function and its properties for this problem are deduced. …”
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The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions by Chuanzhi Bai, Dandan Yang

“…In this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respectively, 0<q<1, 1<β≤α≤2, 0<η1,η2<1, 0<γ1η1α−1<1, and 0<γ2η2β−1<1. …”
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A Family of Integrable Differential-Difference Equations: Tri-Hamiltonian Structure and Lie Algebra of Vector Fields by Ning Zhang, Xi-Xiang Xu

“…Starting from a novel discrete spectral problem, a family of integrable differential-difference equations is derived through discrete zero curvature equation. …”
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Solvability of a Class of Generalized Neumann Boundary Value Problems for Second-Order Nonlinear Difference Equations by Jianye Xia, Yuji Liu

“…New sufficient conditions for the existence of at least one solution of the generalized Neumann boundary value problems for second order nonlinear difference equations ∇Δx(k)=f(k,x(k),x(k+1)), k∈[1,n−1], x(0)=ax(1), x(n)=bx(n−1), are established.…”
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