On the Recursive Sequence xn+1=A+xnp/xn−1p

This paper studies the boundedness, global attractivity, and periodicity of the positive solutions of the difference equation x n + 1 = A + x n p / x n − 1 p , n ∈ ℕ 0 , with p , A ∈ ( 0 , ∞ ) . The main results give a complete picture regarding the boundedness character of the positive solutions of the equation.

[1]  G. Ladas,et al.  On the recursive sequence _{+1}=\frac{}_{}+\frac{1}_{-2} , 1998 .

[2]  Stevo Stevic,et al.  On positive solutions of a (k+1)th order difference equation , 2006, Appl. Math. Lett..

[3]  S. Stevo,et al.  The recursive sequence xn+1 = g(xn, xn-1)/(A + xn) , 2002, Appl. Math. Lett..

[4]  A. M. Ahmed,et al.  On asymptotic behaviour of the difference equation $$X_{N + 1} = \alpha + \frac{{X_{N - 1} ^P }}{{X_N ^P }}$$ , 2003 .

[5]  G. Ladas,et al.  On the Recursive Sequencexn + 1 = α + xn − 1/xn☆ , 1999 .

[6]  Stevo Stević,et al.  Asymptotic behavior of a sequence defined by iteration with applications , 2002 .

[7]  Convergence to equilibria in discrete population models , 2005 .

[8]  Lothar Berg,et al.  Inclusion Theorems for Non-linear Difference Equations with Applications , 2004 .

[9]  Sin-Ei Takahasi,et al.  ON CONVERGENCE OF A RECURSIVE SEQUENCE $x_{n+1} = f(x_{n-1}, x_n)$ , 2006 .

[10]  Kenneth S. Berenhaut,et al.  The behaviour of the positive solutions of the difference equation , 2006 .

[11]  Wan-Tong Li,et al.  Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model , 2005 .

[12]  Stevo Stević.  On the recursive sequence xn+1=-1/xn+A/xn-1 , 2001 .

[13]  Stevo Stević,et al.  On the recursive sequence $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}$$ , 2005 .

[14]  Wan-Tong Li,et al.  On the recursive sequencexn+1=α-(xn/xn−1) , 2005 .

[15]  Stevo Stevi´c,et al.  ON THE RECURSIVE SEQUENCE $x_{n+1}=x_{n-1}/g(x_n)$ , 2002 .