The Dirichlet Problem for a Quasilinear Singularly Perturbed Second Order System

Abstract

We study an equivalent form of the Dirichlet problem for a quasilinear singularly perturbed second order system, which is a singular singularly perturbed boundary value problem. In this way, we have not only eliminated the usual assumption of the existence of a vector potential function, but also proved the existence and uniqueness of the exact solution of the studied problem. Meanwhile, an asymptotic analysis and a remainder estimate of the solution are also presented.