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

• Main Author: Riccardo Molinarolo
• Format: Article
• Language: English
• Published: Texas State University 2019-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlinear non-autonomous transmission problem; singularly perturbed perforated domain; small inclusion; Laplace operator; real analytic continuation in Banach space; asymptotic behaviour
• Online Access: http://ejde.math.txstate.edu/Volumes/2019/53/abstr.html

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 $\epsilon$. We show that the problem has solutions for $\epsilon$ small enough and we investigate the dependence of a specific family of solutions upon $\epsilon$. By adopting a functional analytic approach we prove that the map which takes $\epsilon$ to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.