Asymptotically monotone solutions of a nonlinear difference equation. (English) Zbl 0787.39005

Li, Horng Jaan; Cheng, Sui Sun

Tamkang J. Math. 24, No. 3, 269-282 (1993).

Necessary and sufficient conditions for the eventually positive solutions of a nonlinear difference equation of the type \[ \Delta(p_{n-1}\Delta x_{n-1})+q_ n f(x_ n) =0, \quad n=1,2,3,\dots, \] where \(p_ n>0\) for \(n=0,1,2,\dots\) and \(f\) is a real nondecreasing function defined on \(\mathbb{R}\) such that \(\text{sign} f(x)=\text{sign} x\) to be eventually monotone are derived.

Reviewer: A.D.Mednykh (Novosibirsk)

MSC:

39A10

Additive difference equations

Keywords:

asymptotically monotone solutions; positive solutions; nonlinear difference equation