Bifurcation of periodic solutions to variational inequalities in $\mathbb{R}^\kappa$ based on Alexander-Yorke theorem

Title:

Bifurcation of periodic solutions to variational inequalities in $\mathbb{R}^\kappa$ based on Alexander-Yorke theorem

Creator:

Kučera, Milan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a539b6f7-a969-4219-8986-cebf05e5e149
uuid:a539b6f7-a969-4219-8986-cebf05e5e149

Subject:

bifurcation, periodic solutions, variational inequality, differential inequality, finite dimensional space, and Alexander-Yorke theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Variational inequalities \[ U(t) \in K, (\dot{U}(t)-B_\lambda U(t) - G(\lambda ,U(t)),\ Z - U(t))\ge 0\ \text{for all} \ Z\in \ K, \text{a.a.} \ t\in [0,T) \] are studied, where $K$ is a closed convex cone in $\mathbb{R}^\kappa $, $\kappa \ge 3$, $B_\lambda $ is a $\kappa \times \kappa $ matrix, $G$ is a small perturbation, $\lambda $ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some $\lambda _0$ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some $\lambda _I \ne \lambda _0$. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at $\lambda _0$ constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

449-474

Source:

Czechoslovak Mathematical Journal | 1999 Volume:49 | Number:3

Harvested from:

CDK

Metadata only:

false