A variational property on the evolutionary bifurcation curves for the one-dimensional perturbed Gelfand problem from combustion theory

Abstract

We study a variational property on the evolutionary bifurcation curves for the one-dimensional perturbed Gelfand problem from combustion theory \begin{equation*} \begin{cases} u^{\prime \prime }(x)+\lambda \exp \left( \frac{au}{a+u}\right) =0, & -10$ is the Frank–Kamenetskii parameter or ignition parameter, $a>0$ is the activation energy parameter, and $u$ is the dimensionless temperature.

Keywords

• positive solution
• exact multiplicity
• turning point
• s-shaped bifurcation curve