Abstract
We study the bifurcation curve and exact multiplicity of positive solutions of a two-point boundary value problem arising in a theory of thermal explosion (Equation), where λ > 0 is the Frank-Kamenetskii parameter and a > 0 is the activation energy parameter. By developing some new time-map techniques and applying Sturm's theorem, we prove that, if a > a<sup>∗a∗</sup> ≈ 4.107, the bifurcation curve is S-shaped on the (λ, ||u||∞)-plane. Our result improves one of the main results in Hung and Wang.