On Solutions to a Singular Schrödinger - Maxwell System

Abstract

In this work, we study a doubly singular elliptic system of the form:

-div(B(x)Vu)+v-uino u -div(B(x)Vv) = u=v=0 UY

in

where is an open subset of RN with N≥3, and the parameters y ∈ (0, 1), θ € [0, 1), r≥ 2, and f≥0. The aim of this work is to study the existence of finite-energy solutions for such singular problems. The solutions we seek belong to the Sobolev space H(2)×H) (2). Since the structure of the coupled system generates regularizing effects that give the solutions higher integrability than that provided by the singular theory of a single equation, our study relies on the use of Schauder's fixed point theorem and some basic properties of Sobolev and Lebesgue spaces.