Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality

DOI10.3934/DCDS.2015.35.935zbMath1304.26020arXiv1309.4196OpenAlexW2963932605MaRDI QIDQ477386

Congming Li, Ximing Yin, Genggeng Huang

Publication date: 3 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4196

zbMATH Keywords

existencebest constantconcentration compactnesssupercriticaldiscrete Hardy-Littlewood-Sobolev inequality

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15)

Related Items (8)

REVERSED HARDY–LITTLEWOOD–PÓLYA INEQUALITIES WITH FINITE TERMS ⋮ Existence of normalized solutions for a class of Kirchhoff-Schrödinger-Poisson equations in \(\mathbb{R}^3\) ⋮ The ground state solutions to discrete nonlinear Choquard equations with Hardy weights ⋮ The asymptotic stability of phase separation states for compressible immiscible two-phase flow in 3D ⋮ Critical conditions and asymptotics for discrete systems of the Hardy-Littlewood-Sobolev type ⋮ Existence of solutions for nonlinear biharmonic Choquard equations on weighted lattice graphs ⋮ A nonexistence result for discrete systems related to the reversed Hardy-Littlewood-Sobolev inequality ⋮ The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

Cites Work

• An extended discrete Hardy-Littlewood-Sobolev inequality
• An extension of the Hardy-Littlewood-Pólya inequality
• An optimal summation interval and nonexistence of positive solutions to a discrete system
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• An integral system and the Lane-Emden conjecture
• Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations
• Qualitative properties of solutions for an integral equation
• Regularity of solutions for a system of integral equations
• Radial symmetry of solutions for some integral systems of Wolff type
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Classification of Solutions for a System of Integral Equations
• The best constant in a weighted Hardy-Littlewood-Sobolev inequality
• Classification of solutions for an integral equation

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