Some Crandall–Rabinowitz type results and applications to reaction–diffusion systems

For a small Lipschitz perturbation of a smooth equation the existence of exactly two bifurcation points near a simple eigenvalue is shown. The result is applied to reaction–diffusion systems subject to Turing's diffusion-driven instability under small unilateral obstacles.

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 458; no. 2; pp. 1324 - 1343
Main Author Väth, Martin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2018
Subjects
Crandall–Rabinowitz theorem
Homogenizable operator
Jumping nonlinearity
Nondifferentiable bifurcation
Splitting of bifurcation half-branch
Splitting of critical point
Jumping nonlinearity
Homogenizable operator
Splitting of critical point
Crandall–Rabinowitz theorem
Splitting of bifurcation half-branch
Nondifferentiable bifurcation
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ISSN0022-247X
1096-0813
DOI10.1016/j.jmaa.2017.10.032

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Summary:For a small Lipschitz perturbation of a smooth equation the existence of exactly two bifurcation points near a simple eigenvalue is shown. The result is applied to reaction–diffusion systems subject to Turing's diffusion-driven instability under small unilateral obstacles.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.10.032