Results 21 to 30 of about 5,037 (196)

Ground states of coupled critical Choquard equations with weighted potentials [PDF]

Opuscula Mathematica, 2022
In this paper, we are concerned with the following coupled Choquard type system with weighted potentials \[\begin{cases} -\Delta u+V_{1}(x)u=\mu_{1}(I_{\alpha}\!\ast\![Q(x)|u|^{\frac{N+\alpha}{N}}])Q(x)|u|^{\frac{\alpha}{N}-1}u+\beta(I_{\alpha}\!\ast\![Q(
Gaili Zhu, Chunping Duan, Jianjun Zhang, Huixing Zhang   +3 more
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Integral inequalities with an extended Poisson kernel and the existence of the extremals

Advanced Nonlinear Studies, 2023
In this article, we first apply the method of combining the interpolation theorem and weak-type estimate developed in Chen et al. to derive the Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel.
Tao Chunxia, Wang Yike
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Hardy–Littlewood–Sobolev and related inequalities: Stability

, 2022
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive stability estimates for (HLS).
Dolbeault, Jean, Esteban, Maria J.
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Hardy-Littlewood-Sobolev inequality for $p=1$

Sbornik: Mathematics, 2022
Let $\mathcal{W}$ be a closed dilation and translation invariant subspace of the space of $\mathbb{R}^\ell$-valued Schwartz distributions in $d$ variables. We show that if the space $\mathcal{W}$ does not contain distributions of the type $a\otimes \delta_0$, $\delta_0$ being the Dirac delta, then the inequality $\|\operatorname{I}_\alpha [f]\|_{L_{d ...
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Reversed Stein–Weiss Inequalities with Poisson-Type Kernel and Qualitative Analysis of Extremal Functions

Advanced Nonlinear Studies, 2021
Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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Sharp Hardy–Littlewood–Sobolev inequalities on quaternionic Heisenberg groups [PDF]

Nonlinear Analysis, 2016
26 ...
Christ, Michael, Liu, Heping, Zhang, An
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Ground state sign-changing solutions for critical Choquard equations with steep well potential

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
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The minimizing problem involving $p$-Laplacian and Hardy–Littlewood–Sobolev upper critical exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2018
In this paper, we study the minimizing problem $$ S_{p,1,\alpha,\mu}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - \mu \int_{\mathbb{R}^{N}} \frac{|u|^{p}}{|x|^{p}} \mathrm{d}x} {\left( \int_{\
Yu Su, Haibo Chen
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Reverse Hardy–Littlewood–Sobolev inequalities

Journal de Mathématiques Pures et Appliquées, 2019
This paper is based on the merging of arXiv:1803.06151 and arXiv:1803 ...
Carrillo, José A., Delgadino, Matías G., Dolbeault, Jean, Frank, Rupert L., Hoffmann, Franca   +4 more
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An extended discrete Hardy-Littlewood-Sobolev inequality

Discrete and Continuous Dynamical Systems, 2014
Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: μ=n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for a critical case: μ=n and p=q, by limiting the inequality on a finite domain.
Cheng, Ze, Li, Congming
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