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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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.
|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.|
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|Deposited By:||Kristin Buxton|
|Deposited On:||15 Jan 2009 02:25|
|Last Modified:||26 Dec 2012 10:43|
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