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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A k-Dimensional System of Fractional Finite Difference Equations by Dumitru Baleanu, Shahram Rezapour, Saeid Salehi

“…We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii’s fixed point theorem. …”
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Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane by M. DiPippo, M. R. S. Kulenović

“…We investigate the global dynamics of several anticompetitive systems of rational difference equations which are special cases of general linear fractional system of the forms ., where all parameters and the initial conditions are arbitrary nonnegative numbers, such that both denominators are positive. …”
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Global Asymptotic Stability of a Family of Nonlinear Difference Equations by Maoxin Liao

“…In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)),  n=0,1,…, where ki∈ℕ  (i=1,2,…,v),  v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}. …”
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Oscillation of solutions of impulsive neutral difference equations with continuous variable by Gengping Wei, Jianhua Shen

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Difference Equations and Sharing Values Concerning Entire Functions and Their Difference by Zhiqiang Mao, Huifang Liu

“…The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. …”
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Solutions to some generalized Fermat-type differential-difference equations by Zhiyong Xu, Junfeng Xu

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Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations by E. Thandapani, S. Lourdu Marian, John R. Graef

“…The authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m≥1, n∈ℕ={0,1,2,…}, ani>0 for i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0. …”
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Nonlocal Boundary Value Problems for q-Difference Equations and Inclusions by Sotiris K. Ntouyas, Jessada Tariboon

“…We study boundary value problems for q-difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. …”
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Solving Fractional Difference Equations Using the Laplace Transform Method by Li Xiao-yan, Jiang Wei

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On a Third-Order System of Difference Equations with Variable Coefficients by Stevo Stević, Josef Diblík, Bratislav Iricanin, Zdenek Šmarda

“…We show that the system of three difference equations xn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)), yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), and zn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)), n∈N0, where all elements of the sequences an(i), bn(i), cn(i), n∈N0, i∈{1,2,3}, and initial values x-j, y-j, z-j, j∈{0,1,2}, are real numbers, can be solved. …”
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Some roughness results concerning reducibility for linear difference equations by Garyfalos Papaschinopoulos

“…In this paper we prove first that the exponential dichotomy of linear difference equations is rough. Moreover we prove that if the coefficient matrix of a linear difference equation is almost periodic, then the Joint property of having an exponential dichotomy with a projection P and being reducible with P by an almost periodic kinematics similarity is rough.…”
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Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients by Petr Hasil, Michal Veselý

“…We investigate a type of the Sturm-Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. …”
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Analysis of Random Difference Equations Using the Differential Transformation Method by Şeyma Şişman, Mehmet Merdan

“…The differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. In this study, we apply the theorems related to the DTM to the given examples and investigate the behaviour of the approximate analytical solutions. …”
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