Global attractivity for a class of higher order nonlinear difference equations

摘要

Our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equationxn+1=a−bxnA−∑ki=0bixn−i,n=0,1,…,where A,b,bk∈(0,∞), a,b0,…,bk−1∈[0,∞), k∈{1,2,…} and the initial conditions x−k,…,x0 are arbitrary real numbers. We show that one positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.