Well-defined solutions of a system of difference equations

Haddad, Nabila; Touafek, Nouressadat; Rabago, Julius Fergy T.

doi:10.1007/s12190-017-1081-8

Cited by 22 publications

(9 citation statements)

References 23 publications

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“…ynx n−l . Now we consider the functions 17) which correspond to the equations of (2.3). From (2.16) and (2.17), we can write 19) where m ∈ N 0 , and i ∈ {0, 1, .…”

Section: Theorem 21mentioning

confidence: 99%

Solvability of a system of nonlinear difference equations of higher order

Kara¹,

Yazlık²

2019

Turk J Math

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In this paper, we show that the following higher-order system of nonlinear difference equations, xn = x n−k y n−k−l y n−l (an + bnx n−k y n−k−l) , yn = y n−k x n−k−l x n−l (αn + βny n−k x n−k−l) , n ∈ N0, where k, l ∈ N , (an) n∈N 0 , (bn) n∈N 0 , (αn) n∈N 0 , (βn) n∈N 0 and the initial values x−i, y−i , i = 1, k + l , are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case k = 2, l = k .

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“…ynx n−l . Now we consider the functions 17) which correspond to the equations of (2.3). From (2.16) and (2.17), we can write 19) where m ∈ N 0 , and i ∈ {0, 1, .…”

Section: Theorem 21mentioning

confidence: 99%

Solvability of a system of nonlinear difference equations of higher order

Kara¹,

Yazlık²

2019

Turk J Math

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“…In the meantime, the two-dimensional or threedimensional systems of these equations have become the center of interest of researchers. See, for example, [9,16,17,22,25,34,38,43,45,46,48]. Theoretically, it is very important to characterize the behavior of the solutions of these equations and systems.…”

Section: Introductionmentioning

confidence: 99%

Solvability of a system of higher order nonlinear difference equations

Kara

Yazlık

Tollu

2020

Hacettepe Journal of Mathematics and Statistics

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In this paper we show that the system of difference equations x n = ay n−k + dy n−k x n−(k+l) bx n−(k+l) + cy n−l , y n = αx n−k + δx n−k y n−(k+l) βy n−(k+l) + γx n−l , where n ∈ N 0 , k and l are positive integers, the parameters a, b, c, d, α, β, γ, δ are real numbers and the initial values x −j , y −j , j = 1, k + l, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.

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“…Then, in [37], Equation (1) was extended to the following two-dimensional system of difference equations…”

Section: Introductionmentioning

confidence: 99%