Preprint no. 154
Mathematical Institute of the Academy of Sciences of the Czech Republic

Direction and Stability of Bifurcation Branches
for Variational Inequalities

Jan Eisner, Milan Kucera, Lutz Recke

Jan Eisner, Milan Kucera,  Mathematical Institute, Acad. Sci.of the Czech Republic, 115 67 PRAHA 1, Zitna 25, Czech Republic, e-mail: eisner@math.cas.cz, kucera@math.cas.cz;
Lutz Recke, Institute of Mathematics of the Humboldt University of Berlin, Unter den Linden 6, 10099 BERLIN, Germany recke@mathematik.hu-berlin.de;

Summary:

We consider a class of variational inequalities with a multidimensional parameter under assumptions guaranteeing the existence of smooth families of nontrivial solutions bifurcating from the set of trivial solutions. The direction of bifurcation is shown in a neighbourhood of bifurcation points of a certain type. In the case of potential operators, also the stability and instability of bifurcating solutions and of the trivial solution is described in the sense of minima of the potential. In particular, an exchange of stability is observed.

Keywords:   multiparameter variational inequality, direction of bifurcation, stability of bifurcating solutions, exchange of stability

Mathematics Subject Classification 2000: 35B32, 35J85, 47J15, 47J20.

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