Bifurcation and stability of spatially periodic solutions of nonlinear evolution equations with integral operators
type: Item
instance of: scholarly article
title: Bifurcation and stability of spatially periodic solutions of nonlinear evolution equations with integral operators
zbMATH Open document ID: 0664.45005
DOI: 10.1007/BF02482690
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1987-01-01T00:00:00Z
review text: A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially periodic static bifurcating solutions and their stability. At first, the necessary condition and the sufficient condition for the existence of bifurcation are studied respectively. The stability of the equilibrium solutions is analyzed by the method of semigroups of linear operators. We also obtain the principle of exchange of stability in this case. As an example of application, a concrete result for a special case with integral operators of exponential type is presented.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 4086274
zbMATH Keywords: nonlinear evolution equations
zbMATH Keywords: integral operators
zbMATH Keywords: spatially periodic static bifurcating solutions
zbMATH Keywords: stability
zbMATH Keywords: method of semigroups
author: Q.-S. Lu
MaRDI profile type: Publication
cites work: Q3948194
cites work: Bifurcation, perturbation of simple eigenvalues, and linearized stability
cites work: Q3886065
cites work: Semigroups of linear operators and applications to partial differential equations
full work available at URL: https://doi.org/10.1007/bf02482690
OpenAlex ID: W367241808
description: scientific article; zbMATH DE number 4086274