Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case

We study the nonlinear Schrodinger equation for the s-fractional p-Laplacian strongly coupled with the Poisson equation in dimension two and with p =2s, which is the limiting case for the embedding of the fractional Sobolev space Ws,p(R2). We prove existence of solutions by means of a variational approximating procedure for an auxiliary Choquard equation in which the uniformly approximated sign-changing logarithmic kernel competes with the exponential nonlinearity. Qualitative properties of solutions such as symmetry and decay are also established by exploiting a suitable moving planes technique.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

This article investigates the strongly coupled nonlinear Schrodinger equation and Poisson equation in two dimensions. The existence of solutions is proved using a variational approximating procedure, and qualitative properties of the solutions are established through the moving planes technique.