Solutions to critical equations with a superposition of nonlocal Hartree-type nonlinearities
Year: 2026
Type: preprint
Abstract: We study a class of nonlinear nonlocal elliptic equations in $\mathbb{R}^N$ involving superpositions of Hartree-type nonlinearities. Motivated by the Schrödinger-Poisson-Slater system, these equations arise as natural generalizations of problems with a single nonlocal interaction term. More precisely, we consider equations driven by a family of Riesz potentials weighted by a positive Borel measure, which gives rise to a superposed nonlocal operator. To treat this problem variationally, we introduce suitable functional settings, namely the superposed Coulomb space and the associated superposed Coulomb-Sobolev space, and study their main properties. Combining variational methods with a recently developed scaling-based critical point theory, we prove existence and multiplicity results for radial solutions. We also investigate a Brezis-Nirenberg-type problem and obtain multiplicity results near eigenvalues of an associated nonlinear eigenvalue problem. Our results extend previous works on single Hartree-type equations and provide a unified framework for treating superpositions of nonlocal interactions of Hartree type.
Source: arXiv (Cornell University)
Authors: Marinho, Artur Jorge, Perera, Kanishka
Institution: Florida Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163637711