Existence of periodic solutions for semilinear reaction diffusion systems
type: Item
instance of: scholarly article
title: Existence of periodic solutions for semilinear reaction diffusion systems
zbMATH Open document ID: 1082.35020
author: Norimichi Hirano
author: Sławomir Maciej Rybicki
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-26T00:00:00Z
review text: The paper deals with an autonomous reaction diffusion system of the form \[ \begin{aligned} \dot u(t,x)+\Delta u(t,x)= f(u,v)&\quad\text{in }\mathbb{R}\times\Omega,\\ \dot v(t,x)+\Delta v(t,x)= g(u,v)&\quad\text{in }\mathbb{R}\times\Omega,\\ Bu(t,x)= Bv(t, x)= 0&\quad\text{on }\mathbb{R}\times\partial\Omega, \end{aligned} \] where \(\Omega\subset \mathbb{R}^N\) \((1\leq N\leq 3)\) is a bounded domain with smooth boundary \(\partial\Omega\), \(f\), \(g\) are continuous functions: \(\mathbb{R}\times\mathbb{R}\to\mathbb{R}\) and \(B\) is a Dirichlet or Neumann type boundary operator. For certain type of functions \(f\) and \(g\) the authors are able to show the existence of periodic solutions for some periods.
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K50
zbMATH DE Number: 2119147
zbMATH Keywords: \(S^1\)-degree
zbMATH Keywords: Dirichlet conditions
zbMATH Keywords: Neumann conditions
reviewed by: Vesa Mustonen
MaRDI profile type: Publication
full work available at URL: j.na.2004.08.004
OpenAlex ID: W2047674387
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DOI: 10.1016/J.NA.2004.08.004
description: scientific article; zbMATH DE number 2119147