Title of article :
On the dynamics of a nonautonomous rational difference equation
Author/Authors :
Amine Kerker , Mohamed Laboratory of Applied Mathematics - Badji Mokhtar-Annaba University, Annaba, Algeria , Hadidi, Elbahi Laboratory of Applied Mathematics - Badji Mokhtar-Annaba University, Annaba, Algeria , Salmi, Abdelouahab Laboratory of Applied Mathematics - Badji Mokhtar-Annaba University, Annaba, Algeria
Abstract :
In this paper, we study the following nonautonomous rational difference equation
yn+1=αn+ynαn+yn−k,n=0,1,...,
where {αn}n≥0 is a bounded sequence of positive numbers, k is a positive integer and the initial values y−k,...,y0 are positive real numbers. We give sufficient conditions under which the unique equilibrium y¯=1 is globally asymptotically stable. Furthermore, we establish an oscillation result for positive solutions about the equilibrium point. Our work generalizes and improves earlier results in the literature.
Keywords :
nonautonomous difference equation , global asymptotic stability , oscillation
Journal title :
International Journal of Nonlinear Analysis and Applications
