On the fixed point index and multiple steady-state solutions of reaction- diffusion systems
type: Item
instance of: scholarly article
title: On the fixed point index and multiple steady-state solutions of reaction- diffusion systems
zbMATH Open document ID: 0815.35017
author: W. Feng
author: Wei H. Ruan
published in: Differential and Integral Equations
publication date: 1995-01-30T00:00:00Z
review text: This paper is concerned with the fixed point index of a compact operator and its application to the study of multiple steady-state solutions of nonlinear reaction-diffusion systems. The method is simplified under the condition that the Banach space \(x\) can be decomposed as \(X = Y \oplus S_ \varphi\), which is frequently satisfied by various reaction- diffusion models. A new method for proving the existence of positive steady-state solutions is developed by using this simplified method to semiflows. The result is applied to a three species ecological model for which some sufficient conditions for the existence of positive steady- state solutions are obtained.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 716226
zbMATH Keywords: compact nonlinear operator
zbMATH Keywords: fixed point index
zbMATH Keywords: positive steady-state solutions
zbMATH Keywords: three species ecological model
reviewed by: John F. Toland
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 716226