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Direction and stability of bifurcating solutions for a Signorini problem
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SYSNO ASEP 0437684 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Direction and stability of bifurcating solutions for a Signorini problem Author(s) Eisner, J. (CZ)
Kučera, Milan (MU-W) RID, SAI, ORCID
Recke, L. (DE)Source Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 113, January (2015), s. 357-371Number of pages 15 s. Language eng - English Country GB - United Kingdom Keywords Signorini problem ; variational inequality ; bifurcation direction Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000345687300020 EID SCOPUS 84911864912 DOI 10.1016/j.na.2014.09.032 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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