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Smooth bifurcation branches of solutions for a Signorini problem
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SYSNO ASEP 0354842 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Smooth bifurcation branches of solutions for a Signorini problem Tvůrce(i) Eisner, J. (CZ)
Kučera, Milan (MU-W) RID, SAI, ORCID
Recke, L. (DE)Zdroj.dok. Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 74, č. 5 (2011), s. 1853-1877Poč.str. 25 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova smooth bifurcation ; Signorini problem ; variational inequality Vědní obor RIV BA - Obecná matematika CEP IAA100190805 GA AV ČR - Akademie věd CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000286178200031 EID SCOPUS 78651358121 DOI 10.1016/j.na.2010.10.058 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2011
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