Solutions Form for Some Rational Systems of Difference Equations by H. El-Metwally

“…We deal with the form of the solutions for the following systems of rational difference equations , , with nonzero real numbers initial conditions. …”
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Comparison and oscillation results for delay difference equations with oscillating coefficients by Weiping Yan, Jurang Yan

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Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation by Xiu-Mei Jia, Wan-Tong Li

“…We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: 𝑦𝑛+1=(𝑟+𝑝𝑦𝑛+𝑦𝑛−𝑘)/(𝑞𝑦𝑛+𝑦𝑛−𝑘), 𝑛∈ℕ0, where the parameters 𝑝,𝑞,𝑟∈(0,∞),𝑘∈{1,2,3,…} and the initial conditions 𝑦−𝑘,…,𝑦0∈(0,∞). …”
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On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation by Lili Kong, Huiqin Chen, Luping Li, Shugui Kang

“…In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.…”
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On the Difference Equation xn+1=∑j=0kajfj(xn−j) by Stevo Stevic

“…This paper studies the boundedness character and the global attractivity of positive solutions of the difference equation xn+1=∑j=0kajfj(xn−j),n∈ℕ0, where aj are positive numbers and fj are continuous decreasing self-maps of the interval (0,∞) for j=0,1,…,k.…”
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Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 by Stevo Stević, Bratislav Iričanin

“…The following difference equation xn=xn−lxn−k−1, n∈ℕ0, where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are real numbers, has been investigated so far only for some particular values of k and l. …”
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Existence and Uniqueness of Positive Solitons for a Second-Order Difference Equation by Xinfu Li, Guang Zhang, Ying Wang

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Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation by Guoqiang Dang, Jinhua Cai

“…In this paper, the entire solutions of finite order of the Fermat-type differential-difference equation f″z2+△ckfz2=1 and the system of equations f1″z2+△ckf2z2=1 and f2″z2+△ckf1z2=1 have been studied. …”
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Solvability of a Second Order Nonlinear Neutral Delay Difference Equation by Zeqing Liu, Liangshi Zhao, Jeong Sheok Ume, Shin Min Kang

“…This paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. …”
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Dynamical Behavior of a System of Third-Order Rational Difference Equation by Qianhong Zhang, Jingzhong Liu, Zhenguo Luo

“…This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations xn+1=A+xn/yn-1yn-2, yn+1=A+yn/xn-1xn-2, n=0,1,…, where A∈(0,∞), x-i∈(0,∞); y-i∈(0,∞), i=0,1,2. …”
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Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation by Jia Wei, Xiaoling Han, Fumei Ye

“…We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β, ak,bk are T-periodic functions and akbk>0. …”
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Comparison results and linearized oscillations for higher-order difference equations by G. Ladas, C. Qian

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On a System of Two High-Order Nonlinear Difference Equations by Qianhong Zhang, Wenzhuan Zhang

“…This paper is concerned with dynamics of the solution to the system of two high-order nonlinear difference equations xn+1=xn-k/(q+∏i=0kyn-i), yn+1=yn-k/(p+∏i=0kxn-i), k∈N+, n=0,1,…, where p,q∈(0,∞), x-i∈(0,∞), y-i∈(0,∞) and i=0,1,…,k. …”
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Behavior of a Competitive System of Second-Order Difference Equations by Q. Din, T. F. Ibrahim, K. A. Khan

“…We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: xn+1=(α1+β1xn-1)/(a1+b1yn), yn+1=(α2+β2yn-1)/(a2+b2xn), where the parameters αi, βi, ai, and bi for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. …”
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Existence of Bounded Positive Solutions for Partial Difference Equations with Delays by Zeqing Liu, Zhihua Wu, Young Chel Kwun, Shin Min Kang

“…This paper deals with solvability of the third-order nonlinear partial difference equation with delays Δn(am,nΔm2(xm,n+bm,nxm-τ0,n-σ0))+f(m,n,xm-τ1,m,n-σ1,n,…,xm-τk,m,n-σk,n)=cm,n,  m≥m0,  n≥n0. …”
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Solving a system of nonlinear difference equations with bilinear dynamics by Hashem Althagafi, Ahmed Ghezal

Subjects: “…nonlinear difference equations…”
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Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations by Reza Mokhtari, Fereshteh Toutian Isfahani, Maryam Mohammadi

“…On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs) is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution 𝑢𝑛,𝑚 is constructed by truncating the series to 𝑚 terms. …”
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Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations by Pavel Řehák

“…We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear q-difference equation Dq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0, t∈{qk:k∈N0} with q>1, Φ(u)=|u|α−1sgn⁡u with α>1, to behave like q-regularly varying or q-rapidly varying or q-regularly bounded functions (that is, the functions y, for which a special limit behavior of y(qt)/y(t) as t→∞ is prescribed). …”
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The Solution and Dynamic Behaviour of Difference Equations of Twenty-First Order by Ibrahim Tarek Fawzi Abdelhamid, Dağıstan Şimşek, Burak Oğul

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Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations by Tieshan He, Yimin Lu, Youfa Lei, Fengjian Yang

“…This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.…”
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