Examples of bifurcation of periodic solutions to variational inequalities in $\mathbb {R}^\kappa $

Milan Kučera

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

Milan Kučera (1999)

Czechoslovak Mathematical Journal

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Variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \in [0, T)$ are studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some $λ_{0}$ 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 $λ_{I} \neq λ_{0}$ . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting...

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