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Qualitative stability and solvability of difference equations [PDF]
Linear and Multilinear Algebra, 1991 We develop sufficient conditions for qualitative stability and solvability of the real discrete time system xt+ 1 = Axi + b. These conditions are a combination of qualitative and quantitative criteria and depend on signed digraphs.
Clark Jeffries, P. van den Driessche
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Representations of general solutions to some classes of nonlinear difference equations
Advances in Difference Equations, 2019 Representations of general solutions to three related classes of nonlinear difference equations in terms of specially chosen solutions to linear difference equations with constant coefficients are given.
Stevo Stević +2 more
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Representation of solutions of a solvable nonlinear difference equation of second order
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic +3 more
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Two ways for solving a class of rational second-order difference equations
Advances in Difference Equations, 2019 We consider a class of second-order rational difference equations with two parameters, and we show, in two ways, that the class of equations is solvable in closed form. One way is based on using an invariant for the class of equations, whereas the second
Stevo Stević
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Journal of Inequalities and Applications, 2021 There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied.
Stevo Stević +3 more
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Mathematics, 2022 In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the ...
Teeranush Suebcharoen +2 more
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Energy Reports, 2020 We propose a simple but non-trivial mathematical model of a dam–reservoir system balancing between the downstream environmental management and hydropower production.
Hidekazu Yoshioka
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Solvability of Implicit Difference Equations
, 2015 This article concerns sufficient conditions for the solvability of implicit difference equations. These are cast in a very general framework that relies on the α-covering and Lipschitz properties of the implicit recursive map with respect relatively to the first and second arguments.
Arutyunov A., Pereira F., Zhukovskiy S.
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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner-Pollaczek, continuous Hahn, continuous dual Hahn ...
Sasaki, Ryu +2 more
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Solution of a Solvable System of Difference Equation
Ikonion Journal of Mathematics, 2022 In this study we give solutions for the following difference equation sytem x_{n+1}= (a.x_{n}y_{n-3}/y_{n-2}-\alpha)+\beta y_{n+1}=(b.x_{n-3}y_{n}/x_{n-2}-\beta) +\alpha n ∈N0 where the parameters a,b,, and initial values x_{-i}, y_{-i}, i=0,1,2,3 are non-zero real numbers. We show the asymptotic behavior of the system of equation.
GELİŞKEN, Ali, ARI, Murat
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