Direction and stability of bifurcating solutions for a Signorini problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F15%3A43889018" target="_blank" >RIV/60076658:12310/15:43889018 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/15:00437684 RIV/49777513:23520/15:43928430
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0362546X14003228" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0362546X14003228</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2014.09.032" target="_blank" >10.1016/j.na.2014.09.032</a>

Result language
angličtina
Original language name
Direction and stability of bifurcating solutions for a Signorini problem
Original language description
The equation Delta u+lambda u+ g(lambda, u)u = 0 is considered in a bounded domain in R-2 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 g(lambda, 0) = 0 for lambda is an element of R, lambda 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 lambda(0) from trivialsolutions 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 u(0). In the case when lambda(0) is the first eigenvalue and the branch goes to the right, we show that the bifurcating solutions are asymptotically stable in W-1,W-2-norm. The stability of the trivial solution is also studied and an exchange of stability is obtained.
Czech name
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Czech description
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Type
J<sub>x</sub> - 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/GA13-00863S" target="_blank" >GA13-00863S: Semilinear and Quasilinear Differential Equations: Existence and Multiplicity Results</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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