Results 31 to 40 of about 648,405 (147)
Sharp Hardy–Littlewood–Sobolev inequalities on the octonionic Heisenberg group [PDF]
Calculus of Variations and Partial Differential Equations, 2016 The Hardy-Littlewood-Sobolev inequality for the conjugate exponent on a group of Heisenberg type has the form \[ \left|\iint_{G\times G}\frac{\overline{f(u)}g(v)}{|u^{-1}v|^\lambda}dudv\right|\lesssim\|f\|_p\|g\|_p, \] where ...
Christ, Michael, Liu, Heping, Zhang, An
openaire +1 more source
Extremal problems of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds [PDF]
Journal of Mathematical Analysis and Applications, 2021 This paper studies the existence of extremal problems for the Hardy-Littlewood-Sobolev inequalities on compact manifolds without boundary via Concentration-Compactness principle.
Zhang, Shutao, Han, Yazhou
openaire +3 more sources
Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
doaj +1 more source
Existence of positive solutions to negative power nonlinear integral equations with weights
Boundary Value Problems, 2020 This paper is devoted to the existence and non-existence of positive solutions to the following negative power nonlinear integral equation related to the sharp reversed Hardy–Littlewood–Sobolev inequality: f q − 1 ( x ) = ∫ Ω K ( x ) f ( y ) K ( y ) | x −
Hang Chen, Qianqiao Guo, Qian Wang
doaj +1 more source
On the critical Choquard-Kirchhoff problem on the Heisenberg group
Advances in Nonlinear Analysis, 2022 In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
doaj +1 more source
Biharmonic system with Hartree-type critical nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this article, we investigate the multiplicity results of the following biharmonic Choquard system involving critical nonlinearities with sign-changing weight function: \begin{align*} \begin{cases} \Delta^{2}u = \lambda F(x) |u|^{r-2}u+ H(x)\left ...
Anu Rani, Sarika Goyal
doaj +1 more source
Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes
Journal of Mathematical Analysis and Applications, 2022 We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-compactness principle for stable processes in $\mathbb{R}^N$.
de Pablo, Arturo +2 more
openaire +4 more sources
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
Advances in Nonlinear Analysis, 2021 We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
doaj +1 more source
Reverse Hardy-Littlewood-Sobolev inequalities
, 2018 This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with nonlinear diffusion ...
Dolbeault, Jean +2 more
openaire +2 more sources