Necessary and sufficient conditions for boundedness and stability of N-order difference equation

摘要

We investigate the boundedness, persistence and asymptotic behaviour of the positive solutions of the equationxk+1=A1xkp1+A2xk−1p2+⋯+Anxk−n+1pn,where A1, A2, A3, pi, i=1,2,…,n∈(0,∞) and Ai, i=4,5,…,n∈[0,∞).