Molinarolo, Riccardo2021-11-052021-11-052019-04-22Molinarolo, R. (2019). Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem. <i>Electronic Journal of Differential Equations, 2019</i>(53), pp. 1-29.1072-6691https://hdl.handle.net/10877/14786In 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.Text29 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear non-autonomous transmission problemSingularly perturbed perforated domainSmall inclusionLaplace operatorReal analytic continuation in Banach spaceAsymptotic behaviourArticle