Abstract
We study the bifurcation of positive solutions of a steady-state problem arising in porous-medium combustion: equation presented We give explicit criteria for a unique solution for all λ > 0 when a = 0 and for an S-shaped bifurcation curve when a ≥ 0. We also prove a conjecture of Norbury & Stuart (1987, IMA J. Appl. Math. 39, 241-57).