Global Behavior of a Higher-Order Difference Equation by Tuo Li, Xiu-Mei Jia

“…This paper is concerned with the global behavior of higher-order difference equation of the form 𝑦𝑛+1=(𝑦𝑛∑exp(𝛽(1−2𝑘𝑖=0𝑎𝑖𝑦𝑛−𝑖)))/(1−𝑦𝑛+𝑦𝑛∑exp(𝛽(1−2𝑘𝑖=0𝑎𝑖𝑦𝑛−𝑖))), 𝑛=0,1,2…, 𝑦−𝑘,𝑦−𝑘+1,…,𝑦0∈(0,1). …”
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Asymptotic Periodicity of a Higher-Order Difference Equation by Stevo Stevic

“…We give a complete picture regarding the asymptotic periodicity of positive solutions of the following difference equation: xn=f(xn−p1,…,xn−pk,xn−q1,…,xn−qm), n∈ℕ0, where pi, i∈{1,…,k}, and qj, j∈{1,…,m}, are natural numbers such that p1<p2<⋯<pk, q1<q2<⋯<qm and gcd(p1,…,pk,q1,…,qm)=1, the function f∈C[(0,∞)k+m, (α,∞)], α>0, is increasing in the first k arguments and decreasing in other m arguments, there is a decreasing function g∈C[(α,∞),(α,∞)] such that g(g(x))=x, x∈(α,∞), x=f(x,…,x︸k,g(x),…,g(x)︸m), x∈(α,∞), limx→α+g(x)=+∞, and limx→+∞g(x)=α. …”
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The Stability Cone for a Matrix Delay Difference Equation by M. M. Kipnis, V. V. Malygina

“…We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation 𝑥𝑛=𝐴𝑥𝑛−1+𝐵𝑥𝑛−𝑘. We assume that 𝐴 and 𝐵 are 𝑚×𝑚 simultaneously triangularizable matrices. …”
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Global Attractivity of a Higher-Order Difference Equation by R. Abo-Zeid

“…The aim of this work is to investigate the global stability, periodic nature, oscillation, and the boundedness of all admissible solutions of the difference equation xn+1=Axn-2r-1/(B-C∏i=lkxn-2i), n=0,1,2,… where A,B,C are positive real numbers and l,r,k are nonnegative integers, such that l≤k.…”
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On Stability Analysis of Higher-Order Rational Difference Equation by Abdul Khaliq, H. S. Alayachi, M. S. M. Noorani, A. Q. Khan

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Qualitative Behavior of Rational Difference Equation of Big Order by M. M. El-Dessoky

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On the Dynamics of a Higher-Order Rational Difference Equation by A. M. Ahmed

“…The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equation xn+1=αxn-1/(β+γΠi=lkxn-2ipi),  n=0,1,2,…, where the parameters α,β,γ,pl,pl+1,…,pk are nonnegative real numbers, and l,k are nonnegative integers such that l≤k.…”
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On the Hyers-Ulam Stability of the First-Order Difference Equation by Soon-Mo Jung, Young Woo Nam

“…We prove Hyers-Ulam stability of the first-order difference equation of the form xi+1=F(i,xi), where F is a given function with some moderate features. …”
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On the stability of the linear delay differential and difference equations by A. Ashyralyev, P. E. Sobolevskii

“…We obtain the stability estimates in Hölder norms for the solutions of the initial-value problem of the delay differential and difference equations of the parabolic type.…”
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On the Fractional Difference Equations of Order (2,q) by Jin-Fa Cheng, Yu-Ming Chu

“…This paper presents a kind of new definition of fractional difference, fractional summation, and fractional difference equations and gives methods for explicitly solving fractional difference equations of order (2,q).…”
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Accurate solution estimates for vector difference equations by Rigoberto Medina

“…We also discuss applications of our main results to partial reaction-diffusion difference equations and to a Volterra difference equation.…”
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Stability problem of some nonlinear difference equations by Alaa E. Hamza, M. A. El-Sayed

Subjects: “…Difference Equations…”
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On monotone solutions of some classes of difference equations by Stevo Stevic

“…We describe a method for finding monotone solutions of some classes of difference equations converging to the corresponding equilibria. …”
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On Complex Differential-Difference Equations of Malmquist Type by Jianjun Zhang

“…In this paper, we shall give some properties of complex differential-difference equation of the form ∑μ=1nαμz∏i=1tfz+ciai0μf′z+ciai1μ⋯fkiz+ciaikiμ/∑ν=1mβνz∏i=1tfz+cibi0νf′z+cibi1ν⋯fkiz+cibikiν=Rz,fz, where aijμ μ=1,2,…,n and bijνν=1,2,…,mi=1,2,…,t;j=0,1,…,ki are non-negative integers, cii=1,2,…,t are distinct, nonzero complex numbers, αμzμ=1,2,…,n and βνzν=1,2,…,m are small functions relative to fz, and Rz,fz is a rational function in fz with coefficients, which are small functions of fz. …”
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The Periodic Solutions of a Class of Difference Equations by Qi Wang, Weiling You, Gengrong Zhang

“…In this paper, we study the periodic solutions of a class of difference equations and give a necessary and sufficient condition under which the nonnegative solutions of the equation converge to a 2k-periodic solution by using relevant theoretical knowledge such as upper and lower limits and congruence. …”
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Cm solutions of systems of finite difference equations by Xinhe Liu, Xiuli Zhao, Jianmin Ma

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Periodic Solutions for a System of Difference Equations by Shugui Kang, Bao Shi

“…This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. …”
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Periodic Problems of Difference Equations and Ergodic Theory by B. A. Biletskyi, A. A. Boichuk, A. A. Pokutnyi

“…The necessary and sufficient conditions for solvability of the family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of linear bounded operator in the Banach space and the ergodic theorem. …”
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Asymptotic Behavior of Solutions of Delayed Difference Equations by J. Diblík, I. Hlavičková

“…This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. …”
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On monotone solutions of some classes of difference equations

“…<p>We describe a method for finding monotone solutions of some classes of difference equations converging to the corresponding equilibria. …”
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