Positive solutions for a planar Schrödinger–Poisson system with prescribed mass

Abstract

In this paper, we investigate a planar Schrödinger–Poisson system with prescribed mass on a bounded domain. Under certain assumptions, we prove the existence of positive solutions to the above system by using a fixed point theorem in Carl and Heikkilä (2002). In addition, by employing Moser’s iterative technique, we establish the L∞-bounds on the positive solution of the system.