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Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable

Part of: Boundary value problems

Published online by Cambridge University Press:  09 April 2009

Shin-Hwa Wang  and
Nicholas D. Kazarinoff
Shin-Hwa Wang
Affiliation:
Department of MathematicsNational Tsing Hua UniversityHsinchu, Taiwan300, R.O.C.
Nicholas D. Kazarinoff
Affiliation:
Department of MathematicsNational Tsing Hua UniversityHsinchu, Taiwan300, R.O.C.
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Abstract

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We study the bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the exact number of steady-state solutions which are totally ordered in an order interval. We are then able to find their Conley indices and thus determine their stabilities.

Keywords

bifurcationsteady-state solutionsnonnegative solutionstwo-point boundary value problemstabilityand Conley index.

MSC classification

Secondary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 3 , June 1992 , pp. 343 - 355
Copyright
Copyright © Australian Mathematical Society 1992

References

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