Global continuation of branches of nondegenerate solutions
type: Item
instance of: scholarly article
title: Global continuation of branches of nondegenerate solutions
zbMATH Open document ID: 0594.34020
DOI: 10.1016/0022-0396(86)90110-5
author: B. George
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The author discusses an equation \(-u''=u(1-u)(u-\alpha)\) on [0,L] with Robin boundary conditions. He shows that by varying L,\(\alpha\) and a constant in the boundary conditions in a suitable way, one can join the Dirichlet problem to the Neumann problem such that at each stage all solutions are non-degenerate (and thus the number of solutions remains constant during the homotopy). The proofs depend on a careful study of the time map. He uses this result in some of his work on travelling waves [J. Differ. Equations 61, 335-379 (1986)].
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 3955441
zbMATH Keywords: second order differential equations
zbMATH Keywords: Robin boundary conditions
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Neumann problem
zbMATH Keywords: number of solutions
zbMATH Keywords: time map
zbMATH Keywords: travelling waves
reviewed by: E. N. Dancer
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90110-5
OpenAlex ID: W2056561971
cites work: Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
cites work: Existence of multidimensional travelling wave solutions of an initial boundary value problem
cites work: Non-degenerate solutions of boundary-value problems
cites work: Global bifurcation of steady-state solutions
cites work: Q4746129
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description: scientific article; zbMATH DE number 3955441