On the difference equation \(x_{n+1}=\alpha +\frac{x^p_n}{x^p_{n-1}}\) (Q2471345)

This paper follows a series of work by A. M. Ahmed, R. DeVault, H. El-Owaidy, G. Ladas, M. Mousa et al. on asymptotic behaviors of rational difference equations. The author discusses equilibria, their asymptotic behavior and related dynamics of the difference equation \(x_{n+1}=\alpha+ x_n^p/x_{n-1}^p\), where \(0<p<1\), \(0\le\alpha<\infty\). Then he generalizes to the \((k+1)\)-th order case \(x_{n+1}=\alpha+ x_n^p/x_{n-k}^p\).