Examples of bifurcation of periodic solutions to variational inequalities in ℝ κ

Milan Kučera

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 225-244
  • ISSN: 0011-4642

Abstract

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A bifurcation problem for variational inequalities U ( t ) ∈ K , ( U ˙ ( t ) - B λ U ( t ) - G ( λ , U ( t ) ) , Z - U ( t ) ) ≥ 0 for all Z ∈ K , a.a. t ≥ 0 is studied, where K is a closed convex cone in ℝ κ , κ ≥ 3 , B λ is a κ × κ matrix, G is a small perturbation, λ a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.

How to cite

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Kučera, Milan. "Examples of bifurcation of periodic solutions to variational inequalities in $\mathbb {R}^\kappa $." Czechoslovak Mathematical Journal 50.2 (2000): 225-244. <http://eudml.org/doc/30557>.

@article{Kučera2000,
abstract = {A bifurcation problem for variational inequalities \[ U(t) \in K, (\dot\{U\}(t)-B\_\lambda U(t) - G(\lambda ,U(t)),\ Z - U(t))\ge 0\ \text\{for\} \text\{all\} \ Z\in K, \text\{a.a.\} \ t \ge 0 \] is 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 main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.},
author = {Kučera, Milan},
journal = {Czechoslovak Mathematical Journal},
keywords = {bifurcation; periodic solutions; variational inequality; differential inequality; finite dimensional space; bifurcation; periodic solutions; variational inequality; differential inequality; finite-dimensional space},
language = {eng},
number = {2},
pages = {225-244},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Examples of bifurcation of periodic solutions to variational inequalities in $\mathbb \{R\}^\kappa $},
url = {http://eudml.org/doc/30557},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Kučera, Milan
TI - Examples of bifurcation of periodic solutions to variational inequalities in $\mathbb {R}^\kappa $
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 225
EP - 244
AB - A bifurcation problem for variational inequalities \[ U(t) \in K, (\dot{U}(t)-B_\lambda U(t) - G(\lambda ,U(t)),\ Z - U(t))\ge 0\ \text{for} \text{all} \ Z\in K, \text{a.a.} \ t \ge 0 \] is 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 main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.
LA - eng
KW - bifurcation; periodic solutions; variational inequality; differential inequality; finite dimensional space; bifurcation; periodic solutions; variational inequality; differential inequality; finite-dimensional space
UR - http://eudml.org/doc/30557
ER -

References

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  9. The Hopf Bifurcation Theorem and Applications, Springer, Berlin, 1976. (1976) MR0494309
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