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Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings
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SYSNO ASEP 0486946 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings Author(s) Recke, L. (DE)
Väth, Martin (MU-W) RID, SAI, ORCID
Kučera, Milan (MU-W) RID, SAI, ORCID
Navrátil, J. (CZ)Source Title Patterns of Dynamics. - Cham : Springer, 2017 / Gurevich P. ; Hell J. ; Sandstede B. ; Scheel A. - ISSN 2194-1009 - ISBN 978-3-319-64172-0 Pages s. 184-202 Number of pages 19 s. Publication form Print - P Action International Conference on Patterns of Dynamics Event date 25.07.2016 - 29.07.2016 VEvent location Berlin Country DE - Germany Event type WRD Language eng - English Country CH - Switzerland Keywords nonsmooth equation ; Lipschitz bifurcation branch ; formula for the bifurcation direction Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 EID SCOPUS 85034205258 DOI 10.1007/978-3-319-64173-7_12 Annotation 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... Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
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