Szczegóły publikacji
Opis bibliograficzny
Normalized solutions for Schrödinger equations with critical exponential growth in $R^{2*}$ / Sitong Chen, Vicenţiu D. RǍDULESCU, Xianhua Tang, Shuai Yuan // SIAM Journal on Mathematical Analysis ; ISSN 0036-1410. — 2023 — vol. 55 iss. 6, s. 7704–7740. — Bibliogr. s. 7739–7740, Abstr. — Publikacja dostępna online od: 2023-11-09. — V. Rǎdulescu - dod. afiliacja: Brno University of Technology, Faculty of Electrical Engineering and Communication, Brno, Czech Republic; Department of Mathematics, University of Craiova, Craiova, Romania; ”Simion Stoilow” Institute of Mathematics, Bucharest, Romania; School of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China
Autorzy (4)
- Chen Sitong
- AGHRǎdulescu Vicenţiu
- Tang Xianhua
- Yuan Shuai
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 152201 |
|---|---|
| Data dodania do BaDAP | 2024-04-09 |
| Tekst źródłowy | URL |
| DOI | 10.1137/22M1521675 |
| Rok publikacji | 2023 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | SIAM Journal on Mathematical Analysis |
Abstract
For any a > 0, we study the existence of normalized solutions and ground state solutions to the following Schr\" odinger equation with L2-constraint: \biggl\{ -\int\BbbR\Delta2uu2+dx\lambdau==a,b(x)f(u) x \in \BbbR , where \lambda \in \BbbR is a Lagrange multiplier, the potential b \in \scrC(\BbbR2, (0, \infty)) satisfies 0 < lim|y|\rightarrow\infty b(y) \leq infx\in\BbbR2 b(x) and appears as a converse direction of the Rabinowitz-type trapping potential, and the reaction f \in \scrC(\BbbR, \BbbR) enjoys critical exponential growth of Trudinger-Moser type. Under two different kinds of assumptions on f, we prove several new existence results, which, in the context of normalized solutions, can be considered as both counterparts of planar unconstrained critical problems and extensions of unconstrained Schr\"odinger problems with Rabinowitz-type trapping potential. Especially, in this scenario, we develop some sharp estimates of energy levels and ingenious analysis techniques to restore the compactness which are novel even for b(x) \equiv constant. We believe that these techniques will allow not only treating other L2-constrained problems in the Trudinger-Moser critical setting but also generalizing previous results to the case of variable potentials. © 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.