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Smooth bifurcation branches of solutions for a Signorini problem
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SYSNO ASEP 0354842 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Smooth bifurcation branches of 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. 74, č. 5 (2011), s. 1853-1877Number of pages 25 s. Language eng - English Country GB - United Kingdom Keywords smooth bifurcation ; Signorini problem ; variational inequality Subject RIV BA - General Mathematics R&D Projects IAA100190805 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000286178200031 EID SCOPUS 78651358121 DOI 10.1016/j.na.2010.10.058 Annotation We study a bifurcation problem for the equation Δu+λu+g(λ,u)u=0 on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. Here is the bifurcation parameter, and g is a small perturbation. We prove, under certain assumptions concerning an eigenfunction u0 corresponding to an eigenvalue λ0 of the linearized equation with the same nonlinear boundary conditions, the existence of a local smooth branch of nontrivial solutions bifurcating from the trivial solutions at λ0 in the direction of u0. The contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tool of the proof is a local equivalence of the unilateral BVP to a system consisting of a corresponding classical BVP and of two scalar equations. To this system classical Crandall–Rabinowitz type local bifurcation techniques (scaling and Implicit Function Theorem) are applied. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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