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Zbl 0787.39005
Li, Horng Jaan; Cheng, Sui Sun
Asymptotically monotone solutions of a nonlinear difference equation. (English)
[J] Tamkang J. Math. 24, No.3, 269-282 (1993). ISSN 0049-2930; ISSN 2073-9826/e

Necessary and sufficient conditions for the eventually positive solutions of a nonlinear difference equation of the type $$\Delta(p\sb{n-1}\Delta x\sb{n-1})+q\sb n f(x\sb n) =0, \quad n=1,2,3,\dots, $$ where $p\sb n>0$ for $n=0,1,2,\dots$ and $f$ is a real nondecreasing function defined on $\bbfR$ such that $\text {sign} f(x)=\text {sign} x$ to be eventually monotone are derived.
[A.D.Mednykh (Novosibirsk)]

MSC 2000:: *39A10 Difference equations

Keywords: asymptotically monotone solutions; positive solutions; nonlinear difference equation

Cited in: Zbl 0820.39002

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