Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equation by M. M. El-Dessoky, E. M. Elabbasy, Asim Asiri

“…The main objective of this paper is to study the behavior of the rational difference equation of the fifth-order yn+1=αyn+βynyn-3/(Ayn-4+Byn-3), n=0,1,…, where α,β,A, and B are real numbers and the initial conditions y-4,y-3,y-2,y-1 and y0 are positive real numbers such that Ay-4+By-3≠0. …”
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Global Attractivity and Periodic Character of Difference Equation of Order Four by M. A. Obaid, E. M. Elsayed, M. M. El-Dessoky

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Periodic Solution for a Max-Type Fuzzy Difference Equation by Changyou Wang, Jiahui Li

“…Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. …”
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Fixed Points of Meromorphic Solutions for Some Difference Equations by Zong-Xuan Chen, Kwang Ho Shon

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On the periodic nature of some max-type difference equations by E. M. Elabbasy, H. El-Metwally, E. M. Elsayed

“…We study some qualitative behavior of solutions of some max-type difference equations with periodic coefficients. Some new results of the periodicity character of solutions of that type of difference equations will be established.…”
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Existence of positive solutions for certain partial difference equations by Binggen Zhang, Qiuju Xing

“…We give some sufficient conditions for the existence of positive solutions of partial difference equation aAm+1,n+1+bAm,n+1+cAm+1,n−dAm,n+Pm,nAm−k,n−1=0 by two different methods.…”
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Dynamics of a Family of Nonlinear Delay Difference Equations by Qiuli He, Taixiang Sun, Hongjian Xi

“…We study the global asymptotic stability of the following difference equation: xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…, where 0≤k1<k2<⋯<ks and 0≤m1<m2<⋯<mt with {k1,k2,…,ks}⋂‍{m1,m2,…,mt}=∅, the initial values are positive, and f∈C(Es+t,(0,+∞)) with E∈{(0,+∞),[0,+∞)}. …”
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Asymptotic Stability for a Class of Nonlinear Difference Equations by Chang-you Wang, Shu Wang, Zhi-wei Wang, Fei Gong, Rui-fang Wang

“…We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max⁡⁡{l,k,s,t} and α,a,b,c are positive constants. …”
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Positive Solutions for Systems of Second-Order Difference Equations by Johnny Henderson, Rodica Luca

“…We study the existence and nonexistence of positive solutions of some systems of nonlinear second-order difference equations subject to multipoint boundary conditions which contain some positive constants.…”
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A focal boundary value problem for difference equations by Cathryn Denny, Darrel Hankerson

Subjects: “…difference equation…”
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Oscillations in Difference Equations with Deviating Arguments and Variable Coefficients by G. E. Chatzarakis, H. Péics, I. P. Stavroulakis

“…New sufficient conditions for the oscillation of all solutions of difference equations with several deviating arguments and variable coefficients are presented. …”
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The Robustness of Strong Stability of Positive Homogeneous Difference Equations by The Anh Bui, Dang Xuan Thanh Duong

“…We study the robustness of strong stability of the homogeneous difference equation via the concept of strong stability radii: complex, real and positive radii in this paper. …”
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Variation of constants formulae for difference equations with advanced arguments by Lolimar Díaz, Raúl Naulin

Subjects: “…Difference equations with advanced arguments…”
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Oscillation and nonoscillation theorems for some mixed difference equations by B. Smith, W. E. Taylor

Subjects: “…mixed difference equations…”
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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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