Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 52 (3) , 343-355
- https://doi.org/10.1017/s1446788700035072
Abstract
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
This publication has 11 references indexed in Scilit:
- Bifurcation and stability of positive solutions of a two-point boundary value problemJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1992
- A correction for a paper by J. Smoller and A. WassermanJournal of Differential Equations, 1989
- On the existence of multiple ordered solutions of nonlinear eigenvalue problemsNonlinear Analysis, 1987
- Multiple fixed points of positive mappings.Journal für die reine und angewandte Mathematik (Crelles Journal), 1986
- Bifurcation and stability of stationary solutions of the Fitz-Hugh-Nagumo equationsJournal of Differential Equations, 1986
- Generic bifurcation of steady-state solutionsJournal of Differential Equations, 1984
- Global bifurcation of steady-state solutionsJournal of Differential Equations, 1981
- On multiple positive solutions of nonlinear elliptic eigenvalue problemsCommunications in Partial Differential Equations, 1981
- Symmetry and related properties via the maximum principleCommunications in Mathematical Physics, 1979
- On the Existence of Positive Solutions for a Class of Semilinear Elliptic Boundary Value ProblemsSIAM Journal on Mathematical Analysis, 1979