Monotonicity of solutions converging to a saddle point equilibrium
type: Item
instance of: scholarly article
title: Monotonicity of solutions converging to a saddle point equilibrium
zbMATH Open document ID: 1055.39010
author: Jeffrey T. Hoag
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: The author considers the initial value problem (*) \(y_{n+1}=f(y_{n-1},y_n)\), \(y_{-1},y_0\in I\), where \(f:I\times I\to I\) is a continuously differentiable function. Sufficient conditions are given which assure that every solution of equation (*) which converges to a saddle point equilibrium of (*) is monotone. This result is then applied to a second order rational difference equation.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2093789
zbMATH Keywords: second order difference equation
zbMATH Keywords: saddle point equilibrium
zbMATH Keywords: monotone solution
zbMATH Keywords: rational difference equation
zbMATH Keywords: initial value problem
reviewed by: Pavel Rehak
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.042
OpenAlex ID: W1990740196
cites work: Dynamics of second order rational difference equations. With open problems and conjectures
cites work: On the Trichotomy Character of x n +1 =(α+β x n +γ x n −1 )/( A + x n )
DOI: 10.1016/J.JMAA.2004.01.042
description: scientific article; zbMATH DE number 2093789