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Multiple limit point bifurcation

Decker, Dwight W. and Keller, Herbert B. (1980) Multiple limit point bifurcation. Journal of Mathematical Analysis and Applictions, 75 (2). pp. 417-430. ISSN 0022-247X. doi:10.1016/0022-247X(80)90090-6. https://resolver.caltech.edu/CaltechAUTHORS:20170802-082136797

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Abstract

In this paper we present a new bifurcation or branching phenomenon which we call multiple limit point bifurcation. It is of course well known that bifurcation points of some nonlinear functional equation G(u, λ) = 0 are solutions (u_0, λ_0) at which two distinct smooth branches of solutions, say [u(ε), λ(ε)] and [u^(ε), λ^(ε)], intersect nontangentially. The precise nature of limit points is less easy to specify but they are also singular points on a solution branch; that is, points (u_0, λ_0) = (u(0), λ(0)), say, at which the Frechet derivative G_u^0 ≡ G_u(u_0, λ_0) is singular.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0022-247X(80)90090-6DOIArticle
http://www.sciencedirect.com/science/article/pii/0022247X80900906?via%3DihubPublisherArticle
Additional Information:© 1980 Published by Elsevier Inc. Supported under Contract EY-76-S-03-0767, Project Agreement No. 12 with DOE and by the U.S. Army Research Office under Contract DAAG29-78-C-0011.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)EY-76-S-03-0767
Army Research Office (ARO)DAAG29-78-C-0011
Issue or Number:2
DOI:10.1016/0022-247X(80)90090-6
Record Number:CaltechAUTHORS:20170802-082136797
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170802-082136797
Official Citation:Dwight W Decker, Herbert B Keller, Multiple limit point bifurcation, Journal of Mathematical Analysis and Applications, Volume 75, Issue 2, 1980, Pages 417-430, ISSN 0022-247X, http://dx.doi.org/10.1016/0022-247X(80)90090-6. (http://www.sciencedirect.com/science/article/pii/0022247X80900906)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79737
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Aug 2017 17:42
Last Modified:15 Nov 2021 17:50

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