Bifurcation direction and exchange of stability for variational inequalities on nonconvex sets |
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Authors: | Jan Eisner Milan Kučera Lutz Recke |
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Institution: | 1. Mathematical Institute of the Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Prague 1, Czech Republic;2. Institute of Mathematics of the Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany |
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Abstract: | This paper concerns Crandall–Rabinowitz type bifurcation for abstract variational inequalities on nonconvex sets and with multidimensional bifurcation parameter. We derive formulae which determine the bifurcation direction and, in the case of potential operators, the stability of all solutions close to the bifurcation point. In particular, it follows that in some cases an exchange of stability appears similar to the case of equations, but in some other cases stable nontrivial solutions bifurcate at points where there is no loss of stability of the trivial solution. As an application we consider a system of two second order ODEs with nonconvex unilateral boundary conditions. |
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Keywords: | 35B32 35J85 47J15 47J20 |
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