On oscillation, convergence and boundedness of solutions of some nonlinear difference equations with multiple delay
type: Item
instance of: scholarly article
title: On oscillation, convergence and boundedness of solutions of some nonlinear difference equations with multiple delay
zbMATH Open document ID: 1177.39011
author: Dinh Cong Huong
author: Phan T. Nam
published in: Vietnam Journal of Mathematics
publication date: 2009-05-19T00:00:00Z
review text: In the first part of the paper the authors consider the equation \[ x_{n+1}=\lambda_nx_n+\sum_{i=1}^r\alpha_i(n)F(x_{n-m_i}). \] Various sufficient conditions are established which guarantee oscillation of equation, resp. existence of nonoscillatory solution, resp. the situation where solutions either oscillate or have certain asymptotic behavior. In the second part of the paper, the equation of the form \[ x_{n+1}=G(x_n,x_{n-1},\dots,x_{n-m}) \] is studied. Sufficient conditions are established guaranteeing convergence of every solution to zero (resp. to the positive equilibrium), resp. persistence of every solution.
Mathematics Subject Classification ID: 39A21
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5554979
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: multiple delay
zbMATH Keywords: oscillation
zbMATH Keywords: convergence
zbMATH Keywords: boundedness
zbMATH Keywords: equilibrium
reviewed by: Pavel Rehak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5554979