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 | |||||||||
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| 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. | |||||||||
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| 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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