Results 101 to 110 of about 6,369 (172)

Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity

, 2017
This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{ \begin{split ...
Giacomoni, J., Mukherjee, Tuhina, Sreenadh, K.   +2 more
core  

Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group

, 2014
14 ...
Christ, Michael, Liu, Heping, Zhang, An
openaire   +2 more sources

On the integral systems related to Hardy-Littlewood-Sobolev inequality [PDF]

Mathematical Research Letters, 2007
We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction.
openaire   +2 more sources

Hardy-Littlewood-Sobolev inequality revisit on Heisenberg group

We study a family of fractional integral operators defined on Heisenberg groups. The kernels of these operators satisfy Zygmund dilations. We obtain a Hardy-Littlewood-Sobolev type inequality.
Sun, Chuhan, Wang, Zipeng
openaire   +2 more sources

Regularity for critical fractional Choquard equation with singular potential and its applications

Advances in Nonlinear Analysis
We study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
doaj   +1 more source

On a logarithmic Hartree equation

Advances in Nonlinear Analysis, 2019
We study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree
Bernini Federico, Mugnai Dimitri
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Reverse Stein–Weiss Inequalities on the Upper Half Space and the Existence of Their Extremals

Advanced Nonlinear Studies, 2019
The purpose of this paper is four-fold. First, we employ the reverse weighted Hardy inequality in the form of high dimensions to establish the following reverse Stein–Weiss inequality on the upper half space:
Chen Lu, Lu Guozhen, Tao Chunxia
doaj   +1 more source

A fractional version of Rivière's GL(n)-gauge. [PDF]

Ann Mat Pura Appl, 2022
Da Lio F, Mazowiecka K, Schikorra A.
europepmc   +1 more source

A surprising formula for Sobolev norms. [PDF]

Proc Natl Acad Sci U S A, 2021
Brezis H, Van Schaftingen J, Yung PL.
europepmc   +1 more source

Concentrating solutions for double critical fractional Schrödinger-Poisson system with p-Laplacian in ℝ3

Advances in Nonlinear Analysis
In this article, we consider the following double critical fractional Schrödinger-Poisson system involving p-Laplacian in R3{{\mathbb{R}}}^{3} of the form: εsp(−Δ)psu+V(x)∣u∣p−2u−ϕ∣u∣ps♯−2u=∣u∣ps*−2u+f(u)inR3,εsp(−Δ)sϕ=∣u∣ps♯inR3,\left\{\begin{array}{l}{\
Liang Shuaishuai, Song Yueqiang, Shi Shaoyun   +2 more
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