Existence of Monotone Solutions of a Difference Equation

Abstract EN

We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞).

We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.