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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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • 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

  • Number of pages

    19

  • Pages from-to

    184-202

  • Publisher name

    Springer International Publishing

  • Place of publication

  • Event location

    Free University of Berlin

  • Event date

    Jul 25, 2016

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article