On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) by Taixiang Sun, Hongjian Xi

“…We consider the following nonlinear difference equation: xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞), and {pn}n=0∞ is a positive sequence of the period k+1. …”
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Monotone Iterative Schemes for Positive Solutions of a Fractional q-Difference Equation with Integral Boundary Conditions on the Half-Line by Min Jiang, Rengang Huang

“…In this paper, we study the boundary value problem of a fractional q-difference equation with nonlocal integral boundary conditions on the half-line. …”
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Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero by R. N. Rath, J. G. Dix, B. L. S. Barik, B. Dihudi

“…We find necessary conditions for every solution of the neutral delay difference equation Δ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fn to oscillate or to tend to zero as n→∞, where Δ is the forward difference operator Δxn=xn+1−xn, and pn, qn, rn are sequences of real numbers with qn≥0, rn>0. …”
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A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations by Fueyo, Sébastien, Chitour, Yacine

“…This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [5].…”
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Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian by Xiaofei He

“…By establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(t),…,u(t−n)), n∈ℤ(3), t∈ℤ, has infinitely many homoclinic orbits, where φp(s) is p-Laplacian operator; φp(s)=|s|p−2s(1<p<∞)r, q, f are nonperiodic in t. …”
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Three-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Equations Involving Different Numbers of q by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…We study a new class of three-point boundary value problems of nonlinear second-order q-difference equations. Our problems contain different numbers of q in derivatives and integrals. …”
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Chaotic numerical instabilities arising in the transition from differential to difference nonlinear equations by Alicia Serfaty de Markus

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Nondecreasing bounded continuous solutions of a <mml:math display="inline"><mml:mi>q</mml:mi></mml:math>-difference equation by Hou Yu Zhao, Shan Shan Guo

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Delayed population models with Allee effects and exploitation by Eduardo Liz, Alfonso Ruiz-Herrera

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On the system of two nonlinear difference equations xn+1=A+xn−1/yn,   yn+1=A+yn−1/xn by G. Papaschinopoulos, C. J. Schinas

Subjects: “…System of two nonlinear difference equations…”
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On a class of third order neutral delay differential equations with piecewise constant argument by Garyfalos Papaschinopoulos

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On the Solutions of the System of Difference Equations xn+1=max{A/xn,yn/xn}, yn+1=max{A/yn,xn/yn} by Dağistan Simsek, Bilal Demir, Cengiz Cinar

“…We study the behavior of the solutions of the following system of difference equations xn+1=max⁡{A/xn,yn/xn}, yn+1=max⁡{A/yn,xn/yn} where the constant A and the initial conditions are positive real numbers.…”
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Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

Subjects: “…Numerical instabilities; Difference equations; Lyapunov exponents; Fixed-step schemes; Chaos.…”
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Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization by Krzysztof Fujarewicz, Krzysztof Łakomiec

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Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 by Keying Liu, Peng Li, Weizhou Zhong

“…Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. …”
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Some recent developments on linear determinacy by Carlos Castillo-Chavez, Bingtuan Li, Haiyan Wang

Subjects: “…nonlinear reaction diffusion difference equations.…”
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Optimal harvesting policy for the Beverton--Holt model by Martin Bohner, Sabrina Streipert

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On the Behavior of a System of Rational Difference Equations xn+1=xn-1/(ynxn-1-1),yn+1 = yn-1/(xnyn-1-1),zn+1=1/xnzn-1 by Liu Keying, Wei Zhiqiang, Li Peng, Zhong Weizhou

“…We are concerned with a three-dimensional system of rational difference equations with nonzero initial values. We present solutions of the system in an explicit way and obtain the asymptotical behavior of solutions.…”
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On approximation of the solutions of delay differential equations by using piecewise constant arguments by Istevan Györi

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On the Behavior of Solutions of the System of Rational Difference Equations: 𝑥𝑛+1=𝑥𝑛−1/(𝑦𝑛𝑥𝑛−1−1), 𝑦𝑛+1=𝑦𝑛−1/(𝑥𝑛𝑦𝑛−1−1), and 𝑧𝑛+1=𝑧𝑛−1/(𝑦𝑛𝑧𝑛−1−1) by Abdullah Selçuk Kurbanli

“…We investigate the solutions of the system of difference equations 𝑥𝑛+1=𝑥𝑛−1/(𝑦𝑛𝑥𝑛−1−1), 𝑦𝑛+1=𝑦𝑛−1/(𝑥𝑛𝑦𝑛−1−1), 𝑧𝑛+1=𝑧𝑛−1/(𝑦𝑛𝑧𝑛−1−1), where 𝑦0,𝑦−1,𝑥0,𝑥−1,𝑧−1,𝑧0∈ℝ.…”
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