Szczegóły publikacji
Opis bibliograficzny
A critical fractional Choquard-Kirchhoff problem with magnetic field / Xiang Mingqi, Vicenţiu D. RĂDULESCU, Binlin Zhang // Communications in Contemporary Mathematics ; ISSN 0219-1997. — 2019 — vol. 21 no. 4, s. 1850004-1–1850004-36. — Bibliogr. s. 1850004-34–1850004-36. — V. D. Rădulescu - dod. afiliacja: Department of Mathematics, University of Craiova, Romania
Autorzy (3)
- Mingqi Xiang
- AGHRǎdulescu Vicenţiu
- Zhang Binlin
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 122312 |
|---|---|
| Data dodania do BaDAP | 2019-07-01 |
| DOI | 10.1142/S0219199718500049 |
| Rok publikacji | 2019 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Communications in Contemporary Mathematics |
Abstract
In this paper, we are interested in a fractional Choquard-Kirchhoff-type problem involving an external magnetic potential and a critical nonlinearity M(||u||s,A2)[(-Δ) Asu + u] = λ∫ℝN F(|u|2) |x - y|αdyf(|u|2)u+ |u|2s∗-2uin ℝN, ||u||s,A = ffℝ2N|u(x) - ei(x-y)·A(x+y 2)u(y)|2 |x - y|N+2s dxdy +∫ℝN|u|2dx1/2, where N > 2s with 0 < s < 1, M is the Kirchhoff function, A is the magnetic potential, (-Δ)As is the fractional magnetic operator, f is a continuous function, F(|u|) =∫0|u|f(t)dt, λ > 0 is a parameter, 0 < α <min{N, 4s} and 2s∗ - = 2N N-2s is the critical exponent of fractional Sobolev space. We first establish a fractional version of the concentration-compactness principle with magnetic field. Then, together with the mountain pass theorem, we obtain the existence of nontrivial radial solutions for the above problem in non-degenerate and degenerate cases. © 2019 World Scientific Publishing Company.