Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/67985840:_____/17:00486946 RIV/49777513:23520/17:43950565

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název statě ve sborníku

Patterns of Dynamics

ISBN

978-3-319-64172-0

ISSN

2194-1009

e-ISSN

—

Počet stran výsledku

19

Strana od-do

184-202

Název nakladatele

Springer International Publishing

Místo vydání

—

Místo konání akce

Free University of Berlin

Datum konání akce

25. 7. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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