On some specific nonlinear ordinary difference equations. (English) Zbl 1090.39502

Petropoulou, Eugenia N.

Arch. Math., Brno 36, Suppl., 549-562 (2000).

The problem of the existence of \(l^1\) solutions of various nonlinear difference equations (mostly of the second order, a typical example is the equation \(x(n+2)=\lambda x(n+1)+px(n)\,\text{e}^{-\sigma x(n)}\) with real parameters \(\lambda \in (0,1)\), \(\sigma >0\), \(0<p<(1-\lambda ) \,\text{e}^{{2-\lambda \over 1-\lambda }})\) is investigated. A bound of the solutions and a region of attraction of their equilibrium points are found. The obtained results are proved using a general theorem of the author and P. D. Siafarikas [Comput. Math. Appl. 42, 427–452 (2001; Zbl 1080.39015)].

Reviewer: Ondřej Došlý (Brno)

MSC:

39A10	Additive difference equations
39A11	Stability of difference equations (MSC2000)
32H02	Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables

Keywords:

nonlinear difference equations; bounded solutions; asymptotic stability

Citations:

Zbl 1080.39015