Boundedness character of positive solutions of a higher order difference equation

It is shown that all positive solutions of the difference equation where k is odd, m∈ℕ and A>0 are bounded.

[1]  H. M. El-Owaidy,et al.  On the recursive sequences xn+1=-αxn-1/β±xn , 2003, Appl. Math. Comput..

[2]  Stevo Stevic.  On the difference equation xn+1=alpha + xn-1/xn , 2008, Comput. Math. Appl..

[3]  Stevo Stević.  On the recursive sequence , 2004 .

[4]  Kenneth S. Berenhaut,et al.  THE GLOBAL ATTRACTIVITY OF THE RATIONAL DIFFERENCE EQUATION yn = A+ (yn-k/yn-m)p , 2007 .

[5]  T. Sun,et al.  On boundedness of the solutions of the difference equation xn , 2006 .

[6]  Stevo Stevic,et al.  On a difference equation with min-max response , 2004, Int. J. Math. Math. Sci..

[7]  K. Berenhaut,et al.  A note on the difference equation , 2005 .

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

[9]  Stevo Stević,et al.  Boundedness character of a class of difference equations , 2009 .

[10]  S. Stević,et al.  On the Recursive Sequence x n+1 = α + (βx n−1)/(1 + g(xn )) , 2003 .

[11]  E. Camouzis,et al.  On the boundedness character of rational equations, part 3 , 2007 .

[12]  J. D. Foley,et al.  Quantitative Bounds for the Recursive Sequence y n + 1 = A + , 2005 .

[13]  Kenneth S. Berenhaut,et al.  A note on positive non-oscillatory solutions of the difference equation , 2006 .

[14]  E. Camouzis,et al.  On the boundedness character of rational equations, part 2 , 2006 .

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

[16]  R. Levins,et al.  On the difference equation xn+1=α+βxn−1e−xn , 2001 .

[17]  K. Berenhaut,et al.  The difference equation xn + 1 = α + xn − k ∑ k − 1 i = 0 cixn − i has solutions converging to zero , 2006 .

[18]  G. Ladas,et al.  ON THE RECURSIVE SEQUENCE XN+1 = A/XN+ 1/XN-2 , 1998 .

[19]  S. Ozen,et al.  On the difference equation , 2006 .

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

[21]  C. Kent,et al.  On the Recursive Sequence x n+1= , 2003 .

[22]  Stevo Stević,et al.  On the Behaviour of the Solutions of a Second-Order Difference Equation , 2007 .

[23]  Stevo Stevic,et al.  Quantitative bounds for the recursive sequence yn = A + yn / (yn-k) , 2006, Appl. Math. Lett..

[24]  Alaa E. Hamza,et al.  On the recursive sequence x n+1 =.... , 2008 .

[25]  Kenneth S. Berenhaut,et al.  The global attractivity of the rational difference equation _{}=1+\frac{_{-}}_{-} , 2007 .

[26]  Kenneth S. Berenhaut,et al.  The global attractivity of the rational difference equation $y_n=A+\left(\frac{y_{n-k}}{y_{n-m}}\right)^p$ , 2008 .

[27]  Alaa E. Hamza,et al.  On the recursive sequence xn+1=α+xn−1xn , 2006 .

[28]  Weifeng Su,et al.  On the Recursive Sequence , 2004 .

[29]  Stevo Stevic,et al.  The global attractivity of the rational difference equation yn = (yn-k + yn-m) / (1 + yn-k yn-m) , 2007, Appl. Math. Lett..

[30]  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 .

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

[32]  G. Karakostas,et al.  ON THE RECURSIVE SEQUENCE x_n+1 = α + x_n-k / f(x_n, …, x_n-k_1) , 2005 .

[33]  Stevo Stevi´c,et al.  ON THE RECURSIVE SEQUENCE $x_{n+1}=\displaystyle\frac{A}{\prod^k_{i=0}x_{n-i}}+\displaystyle\frac{1}{\prod^{2(k+1)}_{j=k+2}x_{n-j}}$ , 2003 .

[34]  B. Iričanin.  Dynamics of a Class of Higher Order Difference Equations , 2007 .

[35]  S. Stevo.  Boundedness character of two classes of third-order difference equations(1 , 2009 .

[36]  Bratislav Iričanin,et al.  A Global Convergence Result for a Higher Order Difference Equation , 2007 .

[37]  Lothar Berg,et al.  On the Asymptotics of Nonlinear Difference Equations , 2002 .

[38]  A. M. Ahmed,et al.  On asymptotic behaviour of the difference equation X N+1 = α + X N-1 P /X N P , 2003 .

[39]  J. Feuer.  On the Behavior of Solutions of x n+1 = p+(x n−1/xn ) , 2004 .

[40]  Kenneth S. Berenhaut,et al.  The difference equation xn+1=α+xn−k∑i=0k−1cixn−i has solutions converging to zero , 2007 .

[41]  Stevo Stević.  ON THE RECURSIVE SEQUENCE $x_{n+1} = \dfrac{\alpha + \beta x_{n-k}}{f(x_n,...,x_{n-k+1})}$ , 2005 .

[42]  JOHN D. FOLEY,et al.  THE GLOBAL ATTRACTIVITY OF THE RATIONAL DIFFERENCE , 2005 .

[43]  W. Leighton,et al.  On the Behaviour of Solutions of , 1979 .

[44]  H. M. El-Owaidy,et al.  On asymptotic behaviour of the difference equation xn+1=α+(xn-k/xn) , 2004, Appl. Math. Comput..

[45]  Kenneth S. Berenhaut,et al.  On the rational recursive sequence yn = A + yn-1/yn-m for small A , 2008, Appl. Math. Lett..

[46]  Stevo Stević,et al.  Short Note: A Note on Periodic Character of a Difference Equation , 2004 .

[47]  Alaa E. Hamza,et al.  On the recursive sequence xn+1= , 2008, Comput. Math. Appl..