Regularity for critical fractional Choquard equation with singular potential and its applications
S Liu, J Yang, Y Su - Advances in Nonlinear Analysis, 2024 - degruyter.com
We study the following fractional Choquard equation (− Δ) su+ u∣ x∣ θ=(I α* F (u)) f (u), x∈
RN, where N⩾ 3, s∈ 1 2, 1, α∈(0, N), θ∈(0, 2 s), and I α is the Riesz potential. The main …
RN, where N⩾ 3, s∈ 1 2, 1, α∈(0, N), θ∈(0, 2 s), and I α is the Riesz potential. The main …
On a fractional magnetic pseudorelativistic operator: properties and applications
F Bernini, P d'Avenia - arXiv preprint arXiv:2410.22426, 2024 - arxiv.org
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order
$ s\in (0, 1) $. First we define a suitable functional setting and we prove some fundamental …
$ s\in (0, 1) $. First we define a suitable functional setting and we prove some fundamental …
Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree–Fock theory
We are interested in a general Choquard equation− Δ+ m 2 u− m u+ V (x) u− μ| x| u=∫ RNF
(y, u (y))| x− y| N− α dyf (x, u)− K (x)| u| q− 2 u under suitable assumptions on the bounded …
(y, u (y))| x− y| N− α dyf (x, u)− K (x)| u| q− 2 u under suitable assumptions on the bounded …
On the ground states for the X‐ray free electron lasers Schrödinger equation
H Hu, Y Li, D Zhao - Mathematical Methods in the Applied …, 2023 - Wiley Online Library
We consider the following X‐ray free electron lasers Schrödinger equation (i∇− A) 2 u+ V
(x) u− μ| x| u= 1| x|∗| u| 2 u− K (x)| u| q− 2 u, x∈ ℝ 3,\left (i ∇-A\right) &# x0005E; 2u&# …
(x) u− μ| x| u= 1| x|∗| u| 2 u− K (x)| u| q− 2 u, x∈ ℝ 3,\left (i ∇-A\right) &# x0005E; 2u&# …
Different approaches in Critical Point Theory for entire Schrödinger equations and one for curl-curl problems
F Bernini - 2022 - boa.unimib.it
The purpose of this thesis is to show the results obtained for three Schrödinger type elliptic
partial differential equations. These equations, although sharing the feature of being entire …
partial differential equations. These equations, although sharing the feature of being entire …
Semirelatywistyczne równanie Choquarda z lokalną nieliniowością
B Bieganowski - math.uni.wroc.pl
| u| p− 2u− Γ (x)| u| q− 2u, gdzie m> 0, zaś zewnętrzny potencjał V= Vp+Vl jest sumą ZN-
okresowego potencjału Vp i zanikającego w nieskończoności potencjału Vl. Wykażemy …
okresowego potencjału Vp i zanikającego w nieskończoności potencjału Vl. Wykażemy …