Results 41 to 50 of about 6,369 (172)

Ground state solutions for nonlinearly coupled systems of Choquard type with lower critical exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper, we study the existence of ground state solutions for the following nonlinearly coupled systems of Choquard type with lower critical exponent by variational methods \begin{equation*} \begin{cases} \displaystyle-\Delta u+V(x)u=(I_\alpha\ast ...
Anran Li, Peiting Wang, Chongqing Wei
doaj   +1 more source

Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

Abstract and Applied Analysis, 2014
We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and ...
Linfen Cao, Zhaohui Dai
doaj   +1 more source

On the stability of a version of nonlocal Sobolev inequality

Bulletin of Mathematical Sciences
In this paper, we investigate the stability of the corresponding nonlocal Sobolev inequality ∫ℝN|Δu|2dx≥S∗∫ℝN(|x|−α∗|u|p)updx1p,∀u∈𝒟2,2(ℝN), where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the best constant.
Weiwei Ye, Xinyun Zhang
doaj   +1 more source

Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]

Opuscula Mathematica
In this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
doaj   +1 more source

Sharp reversed Hardy--Littlewood--Sobolev inequality on the half space $\mathbb R_+^n$

, 2016
This is the second in our series of papers concerning some reversed Hardy--Littlewood--Sobolev inequalities. In the present work, we establish the following sharp reversed Hardy--Littlewood--Sobolev inequality on the half space $\mathbb R_+^n$ \[ \int_ ...
Nguyen, Van Hoang, Ngô, Quôc-Anh
core   +1 more source

Function spaces for decoupling

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell, Pierre Portal, Jan Rozendaal, Po‐Lam Yung   +3 more
wiley   +1 more source

Hardy–Littlewood–Sobolev inequalities on compact Riemannian manifolds and applications

Journal of Differential Equations, 2016
In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach.
Yazhou Han, Meijun Zhu
openaire   +2 more sources

Existence of groundstates for Choquard type equations with Hardy–Littlewood–Sobolev critical exponent

Boundary Value Problems, 2021
In this paper, we consider a class of Choquard equations with Hardy–Littlewood–Sobolev lower or upper critical exponent in the whole space R N $\mathbb{R}^{N}$ . We combine an argument of L. Jeanjean and H. Tanaka (see (Proc. Am. Math. Soc. 131:2399–2408,
Xiaowei Li, Feizhi Wang
doaj   +1 more source

The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space [PDF]

, 2007
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant.
Benguria, Rafael D., Frank, Rupert L., Loss, Michael   +2 more
core   +1 more source