Existence, uniqueness and bounds for a problem in combustion theory

A problem in combustion theory consisting of a nonlinear elliptic equation and linear boundary condition is considered. The existence of a non-negative solution is proved and a sufficient condition is given for the uniqueness. Upper and lower bounds for the solutions are obtained by solving linear elliptic equations. These bounds are used as initial functions for an iterative scheme to improve them. Comparison with previous results is obtained whenever possible.