Szczegóły publikacji
Opis bibliograficzny
Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth / Sitong Chen, Vicenţiu D. RĂDULESCU, Xianhua Tang // Mathematische Zeitschrift ; ISSN 0025-5874. — 2024 — vol. 306 iss. 3 art. no. 50, s. 1–32. — Bibliogr. s. 31–32, Abstr. — Publikacja dostępna online od: 2024-02-16. — V. D. Rǎdulescu - dod. afiliacje: Brno University of Technology, Brno, Czech Republic ; University of Craiova, Craiova, Romania ; Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania ; Zhejiang Normal University, Zhejiang, China
Autorzy (3)
- Chen Sitong
- AGHRǎdulescu Vicenţiu
- Tang Xianhua
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 157189 |
|---|---|
| Data dodania do BaDAP | 2024-12-12 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00209-024-03432-9 |
| Rok publikacji | 2024 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Mathematische Zeitschrift |
Abstract
The paper deals with the existence of normalized solutions for the following Schrödinger–Poisson system with L2-constraint: (Formula presented.) where μ>0, λ∈R will arise as a Lagrange multiplier and the nonlinearity enjoys critical exponential growth of Trudinger-Moser type. By specifying explicit conditions on the energy level c, we detect a geometry of local minimum and a minimax structure for the corresponding energy functional, and prove the existence of two solutions, one being a local minimizer and one of mountain-pass type. In particular, to catch a second solution of mountain-pass type, some sharp estimates of energy levels are proposed, suggesting a new threshold of compactness in the L2-constraint. Our study extends and complements the results of Cingolani–Jeanjean (SIAM J Math Anal 51(4): 3533-3568, 2019) dealing with the power nonlinearity a|u|p-2u in the case of a>0 and p>4, which seems to be the first contribution in the context of normalized solutions. Our model presents some new difficulties due to the intricate interplay between a logarithmic convolution potential and a nonlinear term of critical exponential type and requires a novel analysis and the implementation of new ideas, especially in the compactness argument. We believe that our approach will open the door to the study of other L2-constrained problems with critical exponential growth, and the new underlying ideas are of future development and applicability.
