Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima” by S. Hristova, A. Golev, K. Stefanova

“…The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. …”
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Dynamics of a Class of Higher Order Difference Equations by Bratislav D. Iricanin

“…We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1.…”
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Asymptotic behavior of a class of nonlinear difference equations by Stevo Stevic

“…Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S. …”
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Difference equations: From Berry connections to the Coulomb branch by Andrea E. V. Ferrari, Daniel Zhang

“…This action could be quantised to first-order matrix difference equations obeyed by brane amplitudes, and by taking the conformal limit, vortex partition functions. …”
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Stability Analysis of a System of Exponential Difference Equations by Q. Din, K. A. Khan, A. Nosheen

“…We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-yn-1)/(a2+b2xn+c2xn-1), where the parameters αi, βi, γi, ai, bi, and ci for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. …”
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Boundedness of solutions of matrix nonlinear volterra difference equations by Michael I. Gil', Rigoberto Medina

Subjects: “…Volterra difference equations; Boundedness; Estimates for solutions; Matrix.…”
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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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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 and oscillation results for delay difference equations with oscillating coefficients by Weiping Yan, Jurang Yan

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Ulam type stability for nonlinear Hahn difference equations with delay by Kai Chen, Jinrong Wang

Subjects: “…nonlinear hahn difference equation…”
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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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