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].


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