Schrödinger-Poisson systems with zero mass in the Sobolev limiting case

2023/10/12 by Giulio Romani, Romani, Giulio
Computer Science · Mathematics · #35A15 #35J50 #35J60 #35Q55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2310.08460

openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schrödinger equation driven by a weighted N-Laplace operator and without the mass term, and a higher-order fractional Poisson equation. Since the system is considered in \mathbb R^N, the limiting case for the Sobolev embedding, we consider nonlinearities with exponential growth. Existence is proved relying on the study of a corresponding Choquard equation in which the Riesz kernel is a sign-changing logarithm. This is in turn solved by means of a variational approximating procedure for an auxiliary Choquard equation where the logarithm is uniformly approximated by polynomial kernels.

Related

• Nonlocal Schrödinger-Poisson systems in \mathbb R^N: the fractional Sobolev limiting case
• Nonlinear Schrödinger-Poisson systems in dimension two: the zero mass case
• Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
• Quasilinear logarithmic Choquard equations with exponential growth in ℝ^N
• Positive solutions for nonlinear Schrödinger--Poisson Systems with general nonlinearity