Estimates for the norms of solutions of delay difference systems by Rigoberto Medina

“…Applications to partial difference equations, which model diffusion and reaction processes, are given.…”
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A New Part-Metric-Related Inequality Chain and an Application by Xiaofan Yang, Fangkuan Sun, Yuan Yan Tang

“…Part-metric-related (PMR) inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.…”
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Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials by Defang Ma, Zhan Zhou

“…A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. …”
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On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications by Kelong Cheng, Chunxiang Guo, Qingke Zeng

“…Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.…”
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Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model by Zhijian Wei, Meitao Le

“…We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. …”
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On Discrete Fractional Integral Inequalities for a Class of Functions by Saima Rashid, Hijaz Ahmad, Aasma Khalid, Yu-Ming Chu

“…These variants can be utilized as a convenient apparatus in the qualitative analysis of solutions of discrete fractional difference equations. With respect to applications, we can apply the introduced outcomes to explore boundedness, uniqueness, and continuous reliance on the initial value problem for the solutions of certain underlying worth problems of fractional difference equations.…”
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Discrete Weighted Pseudo-Almost Automorphy and Applications by Zhinan Xia

“…As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. …”
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Alpha-Delta Integration and Its Application in Discrete Kinetic Equation Using Mittag–Leffler Factorial Function by Jaraldpushparaj Simon, Sina Etemad, Britto Antony Xavier Gnanaprakasam, İbrahim Avcı

“…The summation and exact form of the solutions related to the special type of difference equations are established in this paper by using the inverse of the delta and alpha-delta operators. …”
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Some Fractional Integral Inequalities for a Generalized Class of Nonconvex Functions by Yeliang Xiao, Muhammad Shoaib Saleem, Faiza Batool

“…Fractional integral inequalities help to solve many difference equations. In this paper, we present some fractional integral inequalities for generalized harmonic nonconvex functions. …”
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Global Attractor of Solutions of a Rational System in the Plane by Miron B. Bekker, Martin J. Bohner, Hristo D. Voulov

“…We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured that every positive solution of this system converges to a finite limit. …”
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A Class of Volterra-Fredholm Type Weakly Singular Difference Inequalities with Power Functions and Their Applications by Yange Huang, Wu-Sheng Wang, Yong Huang

“…An application of the obtained inequalities to the estimation of Volterra-Fredholm type difference equations is given.…”
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Solvability of Nonlocal Fractional Boundary Value Problems by Zhongmin Huang, Chengmin Hou

“…This paper is devoted to introduce a new approach to investigate the existence of solutions for a three-point boundary value problem of fractional difference equations as fllows: , , and = We present an existence result at resonance case. …”
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Multiple Solutions for the Discrete p-Laplacian Boundary Value Problems by Yuhua Long, Haiping Shi

“…By employing a critical point theorem, established by Bonanno, we prove the existence of three distinct solutions to boundary value problems of nonlinear difference equations with a discrete p-Laplacian operator. …”
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An approximation to discrete optimal feedback controls by Jinghao Zhu, Zhiqiang Zou

“…By value functions, we construct difference equations to approximate the optimal control on each interval of small time. …”
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The Hermite polynomials and the Bessel functions from a general point of view by G. Dattoli, H. M. Srivastava, D. Sacchetti

“…We study their relevant recurrence relations and show that they satisfy differential-difference equations which are isospectral to those of the ordinary case. …”
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Some Difference Inequalities for Iterated Sums with Applications by Wu-Sheng Wang, Shanhe Wu

“…These new inequalities can be used as handy tools in the study of the estimation of solutions of difference equations.…”
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A Generalized q-Mittag-Leffler Function by q-Captuo Fractional Linear Equations by Thabet Abdeljawad, Betül Benli, Dumitru Baleanu

“…Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. …”
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Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems by Danfeng Luo, Zhiguo Luo

“…This paper focuses on the uniqueness and novel finite-time stability of solutions for a kind of fractional-order nonlinear difference equations with time-varying delays. Under some new criteria and by applying the generalized Gronwall inequality, the new constructive results have been established in the literature. …”
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A General Discrete Time Model of Population Dynamics in the Presence of an Infection by Giuseppe Izzo, Yoshiaki Muroya, Antonia Vecchio

“…We present a set of difference equations which generalizes that proposed in the work of G. …”
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Global Stability of a Discrete Mutualism Model by Kun Yang, Xiangdong Xie, Fengde Chen

“…By using the iterative method and the comparison principle of difference equations, sufficient conditions which ensure the global asymptotical stability of the interior equilibrium of the system are obtained. …”
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