Periodic Character of Solutions of First Order Nonlinear Difference Equations

2018 ◽  
pp. 59-106
Author(s):  
Michael A. Radin
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
First Order

scholarly journals On a class of solvable difference equations generalizing an iteration process for calculating reciprocals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Iteration Process ◽  
Nonlinear Difference Equation ◽  
Nonlinear Difference Equations ◽  
First Order ◽  
Nonzero Real Number ◽  
Solvable In Closed Form ◽  
The Difference ◽  
Reciprocal Value

AbstractThe well-known first-order nonlinear difference equation $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ y n + 1 = 2 y n − x y n 2 , n ∈ N 0 , naturally appeared in the problem of computing the reciprocal value of a given nonzero real number x. One of the interesting features of the difference equation is that it is solvable in closed form. We show that there is a class of theoretically solvable higher-order nonlinear difference equations that include the equation. We also show that some of these equations are also practically solvable.

scholarly journals Oscillation criteria for first-order forced nonlinear difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Tim Smith
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Oscillation Criteria ◽  
First Order
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