| Title:
|
Bifurcation of periodic solutions to variational inequalities in $\mathbb{R}^\kappa$ based on Alexander-Yorke theorem (English) |
| Author:
|
Kučera, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
449-474 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
bifurcation |
| Keyword:
|
periodic solutions |
| Keyword:
|
variational inequality |
| Keyword:
|
differential inequality |
| Keyword:
|
finite dimensional space |
| Keyword:
|
Alexander-Yorke theorem |
| MSC:
|
34A40 |
| MSC:
|
34A60 |
| MSC:
|
34C23 |
| MSC:
|
34C25 |
| MSC:
|
49J40 |
| MSC:
|
58F14 |
| idZBL:
|
Zbl 1006.49005 |
| idMR:
|
MR1707987 |
| . |
| Date available:
|
2009-09-24T10:24:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127502 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
