A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations by Fanwei Meng

“…We propose a new variable-coefficient Riccati subequation method to establish new exact solutions for nonlinear differential-difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1)-dimensional Toda lattice equation. …”
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Existence of Positive Solutions to Singular 𝑝-Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity by Qiying Wei, You-Hui Su, Subei Li, Xing-Xue Yan

“…These results are new even for the corresponding differential (𝕋=ℝ) and difference equations (𝕋=ℤ), as well as in general time scales setting. …”
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Exponential Stability of Linear Discrete Systems with Multiple Delays by J. Baštinec, H. Demchenko, J. Diblík, D. Ya. Khusainov

“…The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with multiple delays xk+1=Axk+∑i=1sBixk-mi, k=0,1,…, where s∈N, A and Bi are square matrices, and mi∈N. …”
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Fixed Point Property of Variable Exponent Cesàro Complex Function Space of Formal Power Series under Premodular by Awad A. Bakery, Elsayed A. E. Mohamed

“…Finally, real-world examples and applications show solutions to some nonlinear difference equations.…”
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Complex Dynamics in Nonlinear Triopoly Market with Different Expectations by Junhai Ma, Xiaosong Pu

“…A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. …”
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Capturing the Data Uncertainty Change in the Cocaine Consumption in Spain Using an Epidemiologically Based Model by Christopher Anaya, Clara Burgos, Juan-Carlos Cortés, Rafael-J. Villanueva

“…The proposed model is formulated through a nonlinear system of difference equations whose coefficients are treated as stochastic processes. …”
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Trench's Perturbation Theorem for Dynamic Equations by Martin Bohner, Stevo Stevic

“…As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.…”
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Losslessness of Nonlinear Stochastic Discrete-Time Systems by Xikui Liu, Yan Li, Ning Gao

“…This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. …”
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Dynamics and Control on a Discrete Multi-Inventory System by Yuzhen Wang, Li Xu

“…A necessary criterion for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the difference equations of the inventory is obtained. At last, an improved model is put forward.…”
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An Extension of Hypercyclicity for N-Linear Operators by Juan Bès, J. Alberto Conejero

“…We propose an alternative notion of orbit for N-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N-linear operators, for each N≥2. …”
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Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation by Tom H. Koornwinder

“…The last part expands proofs given in Traces of intertwiners for quantum groups and difference equations, I by Etingof and Varchenko, math.QA/9907181. …”
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Existence of Positive Solutions of a Discrete Elastic Beam Equation by Ruyun Ma, Jiemei Li, Chenghua Gao

“…We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞),  and  f:[0,∞)→[0,∞) is continuous. …”
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Modeling of mosquitoes with dominantor recessive Transgenes and Allee effects by Jia Li

“…To study the impact of releasing transgenic mosquitoes on malaria transmission, weformulate discrete-time models for interacting wild and transgenic mosquitoespopulations, based on systems of difference equations. We start with modelsincluding all homozygous and heterozygous mosquitoes. …”
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Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay by J. Diblík, I. Hlavičková

“…We study a frequently investigated class of linear difference equations Δv(n)=−p(n)v(n−k) with a positive coefficient p(n) and a single delay k. …”
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Oscillation for Forced Second-Order Impulsive Nonlinear Dynamic Equations on Time Scales by Mugen Huang, Kunwen Wen

“…As the unification and development of impulsive differential equations and difference equations, impulsive dynamic equations on time scales are a powerful tool to simulate the natural and social phenomena. …”
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Complex dynamics in a simple model of interdependent open economies by Shahriar Yousef, Yuri Maistrenko, Svitlana Popovych

“…Based on a simple two-market model, characterized by a demand link between competitive markets for goods, a system of coupled difference equations is used to represent the interdependent structure of a global economy. …”
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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. …”
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Determining the Geometrical Sizes of Plates with Internal Hinges by Using Additional Conditions by Vildan Yazıcı, Zahir Muradoğlu

“…For a system obtained by placing more than two elastic plates side by side, the transmission conditions are obtained at the common boundaries. Finite difference equations are developed for the problem of plates with internal hinges and applied for determination of the response of a system assembled from three different plates with different mechanical constraints between adjacent plates in this study. …”
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Decision-Making on the Solution of a Stochastic Nonlinear Dynamical System of Kannan-Type in New Sequence Space of Soft Functions by Meshayil M. Alsolmi, Awad A. Bakery

“…Additionally, some successful applications to the existence of solutions of nonlinear difference equations of soft functions are introduced.…”
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On the Definitions of Nabla Fractional Operators by Thabet Abdeljawad, Ferhan M. Atici

“…We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. An alternative definition for the nabla right fractional difference operator is also introduced.…”
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