Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations
type: Item
instance of: scholarly article
title: Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations
zbMATH Open document ID: 0820.39002
DOI: 10.1016/0895-7177(94)00215-A
author: Ravi P. Agarwal
author: Patricia J. Y. Wong
published in: Mathematical and Computer Modelling
publication date: 1995-09-21T00:00:00Z
review text: The authors establish sufficient conditions for the oscillation of all solutions of the perturbed difference equation \[ \Delta(a_{n- 1}(\Delta y_{n- 1})^ \sigma)+ F(n, y_ n)= G(n, y_ n, \Delta y_ n),\quad n\geq 1 \] as well as for the existence of a positive monotone solution of the damped difference equation \[ \Delta(a_ n(\Delta y_ n)^ \sigma)+ b_ n(\Delta y_ n)^ \sigma+ H(n, y_ n, \Delta y_ n)= 0,\quad n\geq 0, \] where \(0< \sigma= p/q\) with \(p\), \(q\) odd integers, or \(p\) even and \(q\) odd integer. For related results see the reviewer [Comput. Math. Appl. 28, No. 1-3, 309-316 (1994; Zbl 0807.39002)] and \textit{H. J. Li} and \textit{S. S. Cheng} [Tamkang J. Math. 24, No. 3, 269-282 (1993; Zbl 0787.39005)].
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 749343
zbMATH Keywords: second-order nonlinear difference equations
zbMATH Keywords: oscillation
zbMATH Keywords: positive monotone solution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 749343