On the difference equation xn+1=axn−l+bxn−k+f(xn−l,xn−k) $x_{n+1}=ax_{n-l}+bx_{n-k}+f ( x_{n-l},x_{n-k} )$

On the difference equation xn+1=axn−l+bxn−k+f(xn−l,xn−k) $x_{n+1}=ax_{n-l}+bx_{n-k}+f ( x_{n-l},x_{n-k} )$

Abstract In this paper, we study the asymptotic behavior of the solutions of a new class of difference equations xn+1=axn−l+bxn−k+f(xn−l,xn−k), $$x_{n+1}=ax_{n-l}+bx_{n-k}+f ( x_{n-l},x_{n-k} ), $$ where l and k are nonnegative integers, a and b are nonnegative real numbers, the initial values x−s,x...

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Bibliographic Details
Main Authors: Mahmoud A. E. Abdelrahman, George E. Chatzarakis, Tongxing Li, Osama Moaaz
Format: Article
Language:English
Published: SpringerOpen 2018-11-01
Series:Advances in Difference Equations
Subjects:
Difference equation
Equilibrium point
Local stability
Periodic solution
Online Access:http://link.springer.com/article/10.1186/s13662-018-1880-8

Internet

http://link.springer.com/article/10.1186/s13662-018-1880-8

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