Mathematical and numerical analysis of a differential equation model for a gas glow discharge

A nonlinear characteristic value problem modeling a gas glow discharge is considered. A small parameter solution is found which corresponds to the classical Schottky equilibrium approximation. The operating characteristic is computed using the small parameter solution as a starting point. Uniqueness of the operating characteristic is inferred from a combination of global mathematical analysis and numerical analysis. The operating characteristic is stable. Finally, an observation on constriction is made.