ON S-SHAPED BIFURCATION CURVES FOR A TWO-POINT BOUNDARY VALUE PROBLEM ARISING IN A THEORY OF THERMAL EXPLOSION

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 [GRAPHICS] where lambda > 0 is the Frank Kamenetskii parameter and alpha > 0 is the activation energy parameter. By developing some new time-map techniques and applying Sturm's theorem, we prove that, if alpha >= alpha ** approximate to 4.107, the bifurcation curve is S-shaped on the (lambda, parallel to u parallel to(infinity))-plane. Our result improves one of the main results in Hung and Wang (J. Differential Equations 251 (2011) 223-237).