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Multiple Solutions of a Generalized Singular Perturbed Bratu Problem

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Multiple Solutions of a Generalized Singular Perturbed Bratu Problem

Bakri, Taoufik, Kuznetsof, Yuri A., 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

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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 > Gina Cody School 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
Digital Object Identifier (DOI):10.1142/S0218127412500952
ID Code:974150
Deposited By: ANDREA MURRAY
Deposited On:14 Jun 2012 20:35
Last Modified:18 Jan 2018 17:37
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