Existence of periodic solutions for a class of nonlinear discrete systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1317.39022
author: Wei Long
author: Wen-Hai Pan
publication date: 2014-11-10T00:00:00Z
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 6367826
zbMATH Keywords: periodic solutions
zbMATH Keywords: nonlinear discrete systems
zbMATH Keywords: sub-super solutions
zbMATH Keywords: Schauder's fixed point theorem
MaRDI profile type: Publication
title: Existence of periodic solutions for a class of nonlinear discrete systems
published in: Journal of Concrete and Applicable Mathematics
review text: The authors consider the following discrete nonautonomous system with delays: NEWLINE\[NEWLINE x_i(n) =\sum_{k=n-r_i}^n f_i(k,x_1(k),\dots,x_m(k)),\;\;i=1,\dots,m, NEWLINE\]NEWLINE where \(r_i\) are positive integers, \(f_i\) are nonnegative \(T\)-periodic with respect to the first variable and continuous with respect to last \(m\) variables function, \(f_i(k,x_1,\dots,x_{i-1},0,x_{i-1},\dots,x_m)=0\), \(i=1,\dots,m\).NEWLINENEWLINEThree theorems on existence of nontrivial \(T\)-periodic solutions to the system are proved. Two illustrative examples are presented.
reviewed by: Oleg Anashkin
description: scientific article; zbMATH DE number 6367826