Existence and regularity of positive solutions for Schrödinger-Maxwell system with singularity

Abstract

In this paper we are going to prove existence for positive solutions of the following Schrödinger-Maxwell system of singular elliptic equations:where Ω is a bounded open set of R N , N > 2, r >, 1, u > 0, ψ > 0, 0 < θ < 1 and f belongs to a suitable Lebesgue space. In particular, we take advantage of the coupling between the two equations of the system by demonstrating how the structure of the system gives rise to a regularizing effect on the summability of the solutions.