Another look at planar Schrodinger-Newton systems

In this paper, we focus on the existence of positive solutions to the following planar Schrodinger-Newton system with general subcritical growth {-delta u + u +phi u = f (u) in R-2,delta phi = u(2) in R-2, where f is a smooth reaction. We introduce a new variational approach, which enables us to study the above problem in the Sobolev space H1(R2). The analysis developed in this paper also allows to investigate the relationship between a Schrodinger-Newton system of Riesz-type and a Schrodinger-Newton system of logarithmic-type. Furthermore, this new approach can provide a new look at the planar Schrodinger-Newton system and may it have some potential applications in various related problems. (C) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This paper focuses on the existence of positive solutions to the planar Schrodinger-Newton system with general subcritical growth, introducing a new variational approach to study the problem in the Sobolev space H1(R2). The analysis also allows investigating the relationship between different types of Schrodinger-Newton systems, providing a new perspective on the system and potential applications in related problems.