On boundedness of the difference equation xn+1=pn+xn-3s+1xn-s+1 with period-k coefficients

摘要

In this note, we study the following non-autonomous equationxn+1=pn+xn-3s+1xn-s+1,n=0,1,…,where pn > 0 is a period-k sequence and s ∈ {1, 2, … } with gcd(3s, k) = 1, and the initial conditions x−3s+1, … , x0 ∈ (0, +∞). We show that every positive solution of this equation is bounded.