Limit Branch of Solutions asp → ∞ for a Family of Sub-Diffusive Problems Related to thep-Laplacian

We characterize the limit as p → ∞ of the branches of solutions to with λ > 0 and , where R < 1. We show that the limit set is a curve of positive viscosity solutions of the equation where and Λ > 0. The key result is a comparison principle for the limit equation from which we deduce uniqueness for the Dirichlet problem and hence the existence of the curve of solutions.