Szczegóły publikacji
Opis bibliograficzny
Ground state solutions of magnetic Schrödinger equations with exponential growth / Lixi Wen, Vicentiu RĂDULESCU, Xianhua Tang, Sitong Chen // Discrete and Continuous Dynamical Systems. Series A ; ISSN 1078-0947. — 2022 — vol. 42 no. 12, s. 5783–5815. — Bibliogr. s. 5813–5815, Abstr. — V. Rǎdulescu - dod. afiliacje: University of Craiova, Craiova, Romania; China-Romania Research Center in Applied Mathema
Autorzy (4)
- Wen Lixi
- AGHRǎdulescu Vicenţiu
- Tang Xianhua
- Chen Sitong
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 144107 |
|---|---|
| Data dodania do BaDAP | 2022-12-22 |
| Tekst źródłowy | URL |
| DOI | 10.3934/dcds.2022122 |
| Rok publikacji | 2022 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete and Continuous Dynamical Systems, Series A |
Abstract
In this paper, we investigate the following nonlinear magnetic Schrödinger equation with exponential growth: (−i∇ + A(x))2u + V (x)u = f(x, |u|2)u in R2, where V is the electric potential and A is the magnetic potential. We prove the existence of ground state solutions both in the indefinite case with subcritical exponential growth and in the definite case with critical exponential growth. In order to overcome the difficulty brings from the presence of magnetic field, by using subtle estimates and establishing a new energy estimate inequality in complex field, we weaken the Ambrosetti-Rabinowitz type condition and the strict monotonicity condition, which are commonly used in the indefinite case. Furthermore, in the definite case, we introduce a Moser type function involving magnetic potential and some new analytical techniques, which can also be applied to related magnetic elliptic equations. Our results extend and complement the present ones in the literature.