Existence of radial stationary solutions for a system in combustion theory (Q717926)

This paper deals with the study of nonnegative radially symmetric solutions of the nonlinear non-cooperative elliptic system \(\Delta u-\varepsilon u+vf(u)=\Delta v-vf(u)=0\) in \({\mathbb R}^3\), such that \(\lim_{|x|\rightarrow\infty}u(x)=0\) and \(\lim_{|x|\rightarrow\infty}v(x)=1\), where \(\varepsilon \geq 0\). This system is inspired by a model for flame balls with radiation losses. This model is based on a one-step kinetic reaction and the system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. The main result of the paper under review establishes the existence of at least two solutions. The key arguments in the proof rely on topological degree tools.