Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00325835" target="_blank" >RIV/68407700:21340/17:00325835 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/17:00486946 RIV/49777513:23520/17:43950565
Result on the web
<a href="https://www.springer.com/us/book/9783319641720" target="_blank" >https://www.springer.com/us/book/9783319641720</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-64173-7_12" target="_blank" >10.1007/978-3-319-64173-7_12</a>
Alternative languages
Result language
angličtina
Original language name
Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings
Original language description
We consider abstract equations of the type F(lambda,u)=tau G(tau,lambda,u), where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that F(lambda,0)=G(tau,lambda,0)=0 for all lambda and tau, F is smooth and the unperturbed equation F(lambda,u)=0 describes a Crandall-Rabinowitz bifurcation in lambda=0, that is, two half-branches of nontrivial solutions bifurcate from the trivial solution in lambda=0. Concerning G, we suppose only a certain Lipschitz condition; in particular, G is allowed to be non-differentiable. We show that for fixed small tau not equal to 0 there exist also two half-branches of nontrivial solutions to the perturbed equation, but they bifurcate from the trivial solution in two bifurcation points, which are different, in general. Moreover, we determine the bifurcation directions of those two half-branches, and we describe, asymptotically as tauto0, how the bifurcation points depend on tau. Finally, we present applications to boundary value problems for quasilinear elliptic equations and for reaction-diffusion systems, both with small non-differentiable terms.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Patterns of Dynamics
ISBN
978-3-319-64172-0
ISSN
2194-1009
e-ISSN
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Number of pages
19
Pages from-to
184-202
Publisher name
Springer International Publishing
Place of publication
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Event location
Free University of Berlin
Event date
Jul 25, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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