## Permanence and global attractivity in nonlinear difference equations.(English)Zbl 0843.39010

Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 1161-1172 (1996).
Summary: We obtain sufficient conditions under which the difference equation $x_{n + 1} = x_n f(x_n, x_{n - k_1}, \dots, x_{n - k_r}), \quad n = 0,1, \dots$ is permanent. We also obtain sufficient conditions under which all positive solutions are attracted to the positive equilibrium of the equation.
For the entire collection see [Zbl 0836.00032].

### MSC:

 39A12 Discrete version of topics in analysis 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 39A10 Additive difference equations