Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings

0486946 - MÚ 2018 RIV CH eng C - Conference Paper (international conference)
Recke, L. - Väth, Martin - Kučera, Milan - Navrátil, J.
Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings.
Patterns of Dynamics. Cham: Springer, 2017 - (Gurevich, P.; Hell, J.; Sandstede, B.; Scheel, A.), s. 184-202. Springer Proceedings in Mathematics & Statistics, 205. ISBN 978-3-319-64172-0. ISSN 2194-1009.
[International Conference on Patterns of Dynamics. Berlin (DE), 25.07.2016-29.07.2016]
Institutional support: RVO:67985840
Keywords : nonsmooth equation * Lipschitz bifurcation branch * formula for the bifurcation direction
OECD category: Pure mathematics
https://link.springer.com/chapter/10.1007/978-3-319-64173-7_12

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...
Permanent Link: http://hdl.handle.net/11104/0281646