On oscillation and nonoscillation properties of Emden-Fowler difference equations
type: Item
instance of: scholarly article
title: On oscillation and nonoscillation properties of Emden-Fowler difference equations
zbMATH Open document ID: 1180.39012
author: M. Cecchi
author: Zuzana Došlá
author: Mauro Marini
published in: Central European Journal of Mathematics
publication date: 2009-11-24T00:00:00Z
review text: The discrete Emden-Fowler equation \[ \Delta(a_n|\Delta x_n|^{\alpha} \operatorname{sgn}\Delta x_n) + b_n|x_{n+1}|^{\beta} \operatorname{sgn}x_{n+1} = 0 \] with \(\alpha>0\), \(\beta>0\) and \(\{a_n\}_n\), \(\{b_n\}_n\) positive real sequences. Set \[ A_n = (a_n)^{-1/\alpha}, \quad Y_a = \sum_{n=0}^{\infty}A_n, \quad Y_b = \sum_{n=0}^{\infty}b_n \] and consider three cases: \[ \begin{aligned} Y_a &= \infty, \quad Y_b<\infty;\tag{H1}\\ Y_a&<\infty, \quad Y_b = \infty;\tag{H2} \\ Y_a&<\infty, \quad Y_b<\infty. \tag{H3}\end{aligned} \] For each of these cases qualitative behavior is analyzed and several examples are given.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 39A21
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 5637483
zbMATH Keywords: Emden-Fowler difference equation
zbMATH Keywords: oscillation
zbMATH Keywords: nonoscillation
zbMATH Keywords: reciprocal principle
MaRDI profile type: Publication
full work available at URL: s11533-009-0014-7
OpenAlex ID: W1971289444
cites work: Q5706757
cites work: Nonoscillatory half-linear difference equations and recessive solutions
cites work: Summation inequalities and half-linear difference equations
cites work: Q3426126
cites work: On the growth of nonoscillatory solutions for difference equations with deviating argument
cites work: Q3398802
cites work: Oscillation of certain two-dimensional nonlinear difference systems
cites work: Oscillation and nonoscillation of two-dimensional difference systems
cites work: Oscillation theorems for second-order nonlinear difference equations.
cites work: Classification schemes for nonoscillatory solutions of two-dimensional nonlinear difference systems
cites work: Q3129022
cites work: Classification schemes for positive solutions to a second-order nonlinear difference equation
DOI: 10.2478/S11533-009-0014-7
description: scientific article; zbMATH DE number 5637483