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Multiple Solutions of Singular Perturbation Problems

Cohen, Donald S. (1972) Multiple Solutions of Singular Perturbation Problems. SIAM Journal on Mathematical Analysis, 3 (1). pp. 72-82. ISSN 0036-1410. http://resolver.caltech.edu/CaltechAUTHORS:COHsiamjma72

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Abstract

Under certain conditions on g(x, u) we establish the existence and asymptotic behavior for small ε > 0 of multiple asymptotic solutions of the nonlinear boundary value problem εu" + u’ - g(x,u) = 0, 0 < x < 1, u’(0) - au(0)= A ≥ 0, a > 0, u’(1) + bu(1) = B > 0, b > 0. Formal techniques of singular perturbation theory clearly reveal the mechanism which controls the appearance of multiple solutions. Their existence is then established rigorously by iteration schemes and the so-called "shooting method" for ordinary differential equations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0503009DOIUNSPECIFIED
Additional Information:© 1972 Society for Industrial and Applied Mathematics. Received by the editors March 9, 1971, and in revised form May 24, 1971. This work was supported in part by the U.S. Army Research Office (Durham) under Contract DAHC 04-68-C-0006 and in part by the National Science Foundation under Grant GP-18471. The author wishes to express his appreciation to Professor Herbert B. Keller for several discussions and helpful suggestions during the course of this work.
Funders:
Funding AgencyGrant Number
Army Research OfficeDAHC 04-68-C-0006
National Science FoundationGP-18471
Record Number:CaltechAUTHORS:COHsiamjma72
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:COHsiamjma72
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12994
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:15 Jan 2009 02:25
Last Modified:26 Dec 2012 10:43

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