论文信息 - On the recursive sequence xn+1 = max{c, xpn/xpn-1}

On the recursive sequence xn+1 = max{c, xpn/xpn-1}

Abstract This work studies the boundedness and global attractivity for the positive solutions of the difference equation x n + 1 = max { c , x n p x n − 1 p } , n ∈ N 0 , with p , c ∈ ( 0 , ∞ ) . It is shown that: (a) there exist unbounded solutions whenever p ≥ 4 , (b) all positive solutions are bounded when p ∈ ( 0 , 4 ) , (c) every positive solution is eventually equal to 1 when p ∈ ( 0 , 4 ) and c ≥ 1 , (d) all positive solutions converge to 1 whenever p , c ∈ ( 0 , 1 ) .

Stevo Stevic | S. Stević

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