J Austral Math Soc Ser A 52 pp343--355, 1992.

Bifurcation of Steady-State Solutions of a Scalar Reaction-Diffusion Equation in One Space Variable

Shin-Hwa Wang and Nicholas D. Kazarinoff

(Received 3 January 1990; revised 7 September 1990)

Abstract

We study the bifurcation of a 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.

1991 AMS Subject Classification: 58F14, 34B15

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Authors

Shin-Hwa Wang
Nicholas D. Kazarinoff: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C.

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Last Modified: Mon Feb 3 9:46:11 2003