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

Kocic, V. L.; Ladas, G.

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

Keywords:

permanence; global attractivity; nonlinear difference equations; positive solutions