Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

Abstract

The set of steady state solutions to a reaction-diffusion equation modeling an autocatalytic chemical reaction is completely determined, when the reactor has spherical geometry, and the spatial dimension is n = 1 or 2 for any reaction order, or n ≥ 3 for subcritical reaction order. Bifurcation approach and analysis of linearized problems are used to establish exact multiplicity and precise global bifurcation diagram of positive steady states. © 2006 Elsevier Inc. All rights reserved.