Original title:
Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings
Authors:
Recke, L. ; Väth, Martin ; Kučera, Milan ; Navrátil, J. Document type: Papers Conference/Event: International Conference on Patterns of Dynamics, Berlin (DE), 20160725
Year:
2017
Language:
eng Abstract:
We consider abstract equations of the type ..., where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that ... for all lambda and tau, F is smooth and the unperturbed equation ... describes a Crandall-Rabinowitz bifurcation in lambda=0, that is, two half-branches of nontrivial solutions bifurcate from the trivial solution in lambda=0. Concerning G, we suppose only a certain Lipschitz condition; in particular, G is allowed to be non-differentiable. We show that for fixed small ... there exist also two half-branches of nontrivial solutions to the perturbed equation, but they bifurcate from the trivial solution in two bifurcation points, which are different, in general. Moreover, we determine the bifurcation directions of those two half-branches, and we describe, asymptotically as ..., how the bifurcation points depend on tau. Finally, we present applications to boundary value problems for quasilinear elliptic equations and...
Keywords:
formula for the bifurcation direction; Lipschitz bifurcation branch; nonsmooth equation Host item entry: Patterns of Dynamics, ISBN 978-3-319-64172-0, ISSN 2194-1009 Note: Související webová stránka: https://link.springer.com/chapter/10.1007/978-3-319-64173-7_12

Institution: Institute of Mathematics AS ČR
(web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences. Original record: http://hdl.handle.net/11104/0281646