Szczegóły publikacji
Opis bibliograficzny
Static solutions for Choquard equations with Coulomb potential and upper critical growth / Sitong Chen, Vicenţiu D. RǍDULESCU, Muhua Shu, Jiuyang Wei // Mathematische Annalen ; ISSN 0025-5831. — 2025 — vol. 392 iss. 2, s. 2081-2130. — Bibliogr. s. 2128-2130, Abstr. — Publikacja dostępna online od: 2025-04-09. — V. Rădulescu - dod. afiliacja: Brno University of Technology, Czech Republic; University of Craiova, Romania; Simion Stoilow Institute of Mathematics of the Romanian Academy
Autorzy (4)
- Chen Sitong
- AGHRǎdulescu Vicenţiu
- Shu Muhua
- Wei Jiuyang
Dane bibliometryczne
| ID BaDAP | 162090 |
|---|---|
| Data dodania do BaDAP | 2025-09-08 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00208-025-03143-4 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Mathematische Annalen |
Abstract
This paper focuses on static solutions for the following Choquard equation with zero mass and Coulomb potential -Delta u +(14/pi|x| & lowast; u(2)) u = mu|u|(p-2)u + (I-alpha & lowast; |u|(alpha+3)) |u|(alpha+1 )u, x is an element of R-3, where mu > 0, 187 < p <= 6, alpha is an element of (0, 3), alpha + 3 is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, I-alpha:R-3 -> R is the Riesz potential, and 1/4 pi|x| is the Coulomb potential. By carefully analyzing the intricate interplay between the power and Coulomb terms, we establish three types of variational geometries of the problem and prove the following existence results based on the behavior of p: (1) the existence of two solutions, one being a local minimizer and the other of mountain-pass type, for an explicit range 0 < mu < Const. when 18/7 < p < 3; (2) the existence of a positive solution if mu takes some particular value when p = 3; (3) the existence of a ground state solution for all mu > 0 when 4 < p < 6, and for two explicit ranges mu > Const. when 3 < p < 4 and p = 4. Furthermore, we obtain a non-existence result for the case p = 6. Particularly, we identify different compactness thresholds for above three cases, and introduce three types of test functions to control the corresponding minimax levels to be less than prescribed thresholds, thereby overcoming the loss of compactness arising from the nonlocal critical term. The derivation of these strict inequalities is a novel contribution and constitutes one of the noteworthy highlights of this work, which is available and new for the limiting Sobolev critical problem as alpha -> 0. We believe that the underlying ideas have potential for future development and can be applied to a broader range of variational problems with critical growth.
