Solvability and representations of the general solutions to some nonlinear difference equations of second order

Stevo Stević; Stevo Stević

doi:10.3934/math.2023773

AIMS Mathematics

2023, Volume 8, Issue 7: 15148-15165. doi: 10.3934/math.2023773

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Solvability and representations of the general solutions to some nonlinear difference equations of second order

Stevo Stević ^{1,2
,
,}

1.
Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/Ⅲ, Beograd 11000, Serbia
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 06 February 2023 Revised: 31 March 2023 Accepted: 06 April 2023 Published: 23 April 2023
MSC : 39A20

We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order considered in the literature, present an extension of the class of difference equations which is solvable in closed form, analyze some results on the long-term behavior of the solutions to the class of equations, and give some results on convergence.
- difference equation,
- solvable equation,
- closed-form formula for solutions,
- bilinear difference equation
Citation: Stevo Stević. Solvability and representations of the general solutions to some nonlinear difference equations of second order[J]. AIMS Mathematics, 2023, 8(7): 15148-15165. doi: 10.3934/math.2023773

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Abstract

We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order considered in the literature, present an extension of the class of difference equations which is solvable in closed form, analyze some results on the long-term behavior of the solutions to the class of equations, and give some results on convergence.

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