Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

Abstract EN

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn+1=(r+pyn+yn−k)/(qyn+yn−k), n∈ℕ0, where the parameters p,q,r∈(0,∞),k∈{1,2,3,…} and the initial conditions y−k,…,y0∈(0,∞).

We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.