Second Order Nonlinear Singular Perturbation Problems with Boundary Conditions of Mixed Type

Abstract

We study nonlinear turning point problems that admit boundary and/or interior layers at positions that are not determined a priori. Our study differs from previous investigations in that for positive “viscosity” first order derivative terms are allowed in the boundary operator. Under certain conditions, shown in a sense to be sharp, we characterize the viscous limit of such problems and prove that they are identical to those limit solutions obtained from the pure Dirichlet problem.