Bakri, Taoufik and Kuznetsof, Yuri A. and Verhurst, Ferdinand and Doedel, Eusebius (2012) Multiple Solutions of a Generalized Singular Perturbed Bratu Problem. International Journal of Bifurcation and Chaos, 22 (04). pp. 1250095-1. ISSN 0218-1274
![[img]](http://spectrum.library.concordia.ca/style/images/fileicons/application_pdf.png)
| PDF - Accepted Version 166Kb |
Official URL: http://dx.doi.org/10.1142/S0218127412500952
Abstract
Nonlinear two-point boundary value problems (BVPs) may have none or more than one solution. For the singularly perturbed two-point BVP εu″ + 2u′ + f(u) = 0, 0 < x < 1, u(0) = 0, u(1) = 0, a condition is given to have one and only one solution; also cases of more solutions have been analyzed. After attention to the form and validity of the corresponding asymptotic expansions, partially based on slow manifold theory, we reconsider the BVP within the framework of small and large values of the parameter. In the case of a special nonlinearity, numerical bifurcation patterns are studied that improve our understanding of the multivaluedness of the solutions.
| Divisions: | Concordia University > Faculty of Engineering and Computer Science > Computer Science and Software Engineering |
|---|---|
| Item Type: | Article |
| Refereed: | Yes |
| Authors: | Bakri, Taoufik and Kuznetsof, Yuri A. and Verhurst, Ferdinand and Doedel, Eusebius |
| Journal or Publication: | International Journal of Bifurcation and Chaos |
| Date: | 2012 |
| ID Code: | 974150 |
| Deposited By: | ANDREA MURRAY |
| Deposited On: | 14 Jun 2012 16:35 |
| Last Modified: | 14 Jun 2012 16:35 |
Repository Staff Only: item control page
