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Direction and stability of bifurcating solutions for a Signorini problem

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    0437684 - MÚ 2016 RIV GB eng J - Journal Article
    Eisner, J. - Kučera, Milan - Recke, L.
    Direction and stability of bifurcating solutions for a Signorini problem.
    Nonlinear Analysis: Theory, Methods & Applications. Roč. 113, January (2015), s. 357-371. ISSN 0362-546X. E-ISSN 1873-5215
    Institutional support: RVO:67985840
    Keywords : Signorini problem * variational inequality * bifurcation direction
    Subject RIV: BA - General Mathematics
    Impact factor: 1.125, year: 2015

    The equation ... is considered in a bounded domain in R2R2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that ... for ... is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation branch of non-trivial solutions emanating at ... from trivial solutions is studied. We show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u0u0. In the case when ... is the first eigenvalue and the branch goes to the right, we show that the bifurcating solutions are asymptotically stable in W1,2W1,2-norm. The stability of the trivial solution is also studied and an exchange of stability is obtained.
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