Smooth bifurcation branches of solutions for a Signorini problem

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00354842" target="_blank" >RIV/67985840:_____/11:00354842 - isvavai.cz</a>

Alternative codes found

RIV/60076658:12310/11:43881736

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Smooth bifurcation branches of solutions for a Signorini problem

Original language description

We study a bifurcation problem for the equation ?u+?u+g(?,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 ?0 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 ?0 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/IAA100190805" target="_blank" >IAA100190805: Bifurcation and parameter dependence for unilateral boundary value problems and interpretation in natural sciences</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

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Volume of the periodical

74

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

25

Pages from-to

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UT code for WoS article

000286178200031

EID of the result in the Scopus database

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