## Abstract

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form

is investigated, where all the coefficients are nonnegative real numbers.

### Similar content being viewed by others

## References

R.P.Agarwal,

*Difference equations and inequalities*, 2nd Edition, Pure Appl. Math. 228, Marcel Dekker, New York, 2000.A.M.Amleh, E.A.Grove, G.Ladas and D.A.Georgion, On the recursive sequence\(y_{n + 1} = \alpha + \frac{{y_{n - 1} }}{{y_n }}\), J. Math. Anal. Appl.

**233**(1999), 790–798.H.M.El-Owaidy, A.M.Ahmed and M.S.Mousa, On asymptotic behaviour of the difference equation\(x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}\), J. Appl. Math. & Computing

**12**(1–2) (2003), 31–37.M.R.S.Kulenović and G.Ladas,

*Dynamics of Second Order Rational Difference Equations*, Chapman & Hall/CRC, (2001).G.Ladas,

*Open problems and conjectures*, J. Differ. Equations Appl.**5**(1999), 211–215.S.Stević,

*On the recursive sequence x*_{ n+1}=*g*(*x*_{ n },*x*_{ n−1})/(*A*+*x*_{ n }), Appl. Math. Lett.**15**(2002), 305–308.S.Stević,

*On the recursive sequence x*_{ n+1}=*x*_{ n−1}/*g*(*x*_{ n }), Taiwanese J. Math.**6**(3) (2002), 405–414.Z.Zhang, B.Ping and W.Dong,

*Oscillatory of unstable type second-order neutral difference equations*, J. Appl. Math. & Computing**9**No. 1 (2002), 87–100.Z.Zhou, J.Yu and G.Lei,

*Oscillations for even-order neutral difference equations*, J. Appl. Math. & Computing**7**No. 3 (2000), 601–610.

## Author information

### Authors and Affiliations

### Corresponding author

## Additional information

**Stevo Stević** received his Ph.D at Belgrade University in 2001. He has written more than 80 original scientific papers and his research interests are mostly in analytic functions of one and several variables, potential theory, difference equations, convergence and divergence of infinite limiting, nonlinear analysis, fixed point theory, operators on function spaces, inequalities and qualitative analysis of differential equations.

## Rights and permissions

## About this article

### Cite this article

Stević, S. On the recursive sequence\(x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}\)
.
*JAMC* **18**, 229–234 (2005). https://doi.org/10.1007/BF02936567

Received:

Revised:

Issue Date:

DOI: https://doi.org/10.1007/BF02936567