Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem

Abstract

In this article we analyze a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size ε. We show that the problem has solutions for ε small enough and we investigate the dependence of a specific family of solutions upon ε. By adopting a functional analytic approach we prove that the map which takes ε to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.