Traveling wave solutions in delayed lattice differential equations with partial monotonicity
type: Item
instance of: scholarly article
title: Traveling wave solutions in delayed lattice differential equations with partial monotonicity
zbMATH Open document ID: 1084.34059
author: Gang Lü
author: Shigui Ruan
author: Jian Hua Huang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: Delayed lattice differential equations can be seen as the discrete version of delayed reaction-diffusion equations. In this nice paper, the authors study existence of traveling wave solutions for a system of two delayed lattice differential equations, and generalize some previous results due to \textit{J. Wu} and \textit{X. Zou} [J. Differ. Equations 135, No.2, 315-357 (1997; Zbl 0877.34046)], by relaxing the monotonicity assumptions. The main tool in their proofs is the application of Schauder's fixed-point theorem to an abstract operator defined in an appropriate subset of \(C(\mathbb{R},\mathbb{R}^2)\) endowed with an exponential decay norm.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 2136808
zbMATH Keywords: Schauder's fixed-point theorem
zbMATH Keywords: traveling wave solution
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: quasimonotonicity
MaRDI profile type: Publication
full work available at URL: j.na.2004.10.020
OpenAlex ID: W2059099102
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DOI: 10.1016/J.NA.2004.10.020
description: scientific article; zbMATH DE number 2136808