Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations by Shu-Yu Yang, Guo-Cheng Wu

Subjects: “…delay fractional difference equations…”
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Discrete Weighted Pseudo Almost Automorphic Solutions of Nonautonomous Difference Equations by Xiaoqing Wen, Hongwei Yin

“…Further, we investigate the nonautonomous linear and semilinear difference equations and obtain the weighted pseudo almost automorphic solutions of both these kinds of difference equations, respectively. …”
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Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces by Anna Kisiolek, Ireneusz Kubiaczyk

“…We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1)+pnf(xn−k)=hn. …”
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On Some New Fixed Point Results with Applications to Matrix Difference Equations by Marwan Amin Kutbi, Jamshaid Ahmad, Muhammad Imran Shahzad

“…Some convergence results for a class of matrix difference equations will be derived as application.…”
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On Linear Difference Equations for Which the Global Periodicity Implies the Existence of an Equilibrium by István Győri, László Horváth

“…It is proved that any first-order globally periodic linear inhomogeneous autonomous difference equation defined by a linear operator with closed range in a Banach space has an equilibrium. …”
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Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients by Durhasan Turgut Tollu

“…This paper is dealt with the following system of difference equations xn+1=an/xn+bn/yn,yn+1=cn/xn+dn/yn, where n∈ℕ0=ℕ∪0, the initial values x0 and y0 are the positive real numbers, and the sequences ann≥0, bnn≥0, cnn≥0, and dnn≥0 are two-periodic and positive. …”
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Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) by Awad A. Bakery

“…We give in this work the sufficient conditions on the positive solutions of the difference equation xn+1=α+(xn-1m/xnk),  n=0,1,…, where α, k, and m∈(0,∞) under positive initial conditions x-1,  x0 to be bounded, α-convergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution. …”
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On the order of exponential growth of the solution of the linear difference equation with periodic coefficient in Banach space by H. Attia Hussein

Subjects: “…difference equations…”
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The Neimark–Sacker Bifurcation and Global Stability of Perturbation of Sigmoid Beverton–Holt Difference Equation by M. R. S. Kulenović, Connor O’Loughlin, E. Pilav

“…This difference equation is one of the perturbations of the sigmoid Beverton–Holt difference equation, which is a major mathematical model in population dynamics. …”
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Analytical solution of a class of coupled second order differential-difference equations by L. Jódar, J. A. Martin Alustiza

Subjects: “…differential-difference equation…”
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Roughness of (ℤ+,ℤ-)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces by Nicolae Lupa

“…In this paper we study the roughness of (ℤ+,ℤ-)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. …”
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Boundary Value Problems for Fourth Order Nonlinear p-Laplacian Difference Equations by Qinqin Zhang

“…We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation containing both advance and retardation. …”
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The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations by Khaled A. Gepreel, Taher A. Nofal, Ali A. Al-Thobaiti

“…Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.…”
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Asymptotics and Periodicity of Positive Solutions on a Nonlinear Rational System of Difference Equations by Weizhen Quan, Xiaomei Lu, Li Wang, Jingren Zhou, Ridi Huang

“…The purpose of this paper is to discuss a nonlinear rational difference equation system with three variables. Firstly, by utilizing Jacobian theory, the stability of the system is obtained. …”
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About the Stability and Positivity of a Class of Discrete Nonlinear Systems of Difference Equations by M. De la Sen

“…This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. …”
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A Hille-Wintner type comparison theorem for second order difference equations by John W. Hooker

Subjects: “…difference equations…”
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Some New Oscillation Criteria for Fourth-Order Nonlinear Delay Difference Equations by Kandasamy Alagesan, Subaramaniyam Jaikumar, Govindasamy Ayyappan

“…In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation Δc3nΔc2nΔc1nΔun+pnfun−k=0 under the conditions ∑n=n0∞cin<∞, i=1, 2, 3. …”
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Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions by Chengmin Hou, Sui Sun Cheng

“…For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. …”
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Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method by Faizan Ahmad Khan

“…Finally, the solution of a nonlinear fractional difference equation is approximated via the proposed iterative method. …”
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The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions by Yanping Guo, Xuefei Lv, Yude Ji, Yongchun Liang

“…We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)),  k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where a,b>0 and Δu(k)=u(k+1)-u(k) for k∈{0,1,…,n-1},  f:{0,1,…,n}×[0,+∞)→[0,+∞) is continuous. h(i) is nonnegative i∈{2,3,…,n+2}; g(i) is nonnegative for i∈{0,1,…,n}. …”
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