On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents

2016/05/17 by Fashun Gao, Gao, Fashun, Minbo Yang +1 · 4 citations
Mathematics · #35J25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Boundary (topology) #Bounded function #Combinatorics #Critical exponent #Dirichlet boundary condition #Domain (mathematical analysis) #Exponent #FOS: Mathematics #Geometry #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Multiplicity (mathematics) #Nehari manifold #Nonlinear Partial Differential Equations #Nonlinear system #Omega #Physics #Quantum mechanics #Sobolev space #math.AP #msc:35J25

paper · pdf · doi:10.48550/arxiv.1605.05038

published in arXiv (Cornell University) (Cornell University) · 30

openalex publication_date 2016/05/17 · arxiv created 2016/10/30 · arxiv updated 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the following nonlinear Choquard equation with Dirichlet boundary condition -Δu =(∫_Ω\frac|u|^2_μ^∗|x-y|^μdy)|u|^2_μ^∗-2u+λf(u)\hspace4.14mmin\hspace1.14mm Ω, where Ω is a smooth bounded domain of ℝ^N, λ>0, N≥3, 0

Cited by

• On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent
• Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential
• Normalized solutions to a Choquard equation involving mixed local and nonlocal operators
• p-biharmonic Kirchhoff equations with critical Choquard nonlinearity

Related

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• On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
• Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential
• Critical exponent Neumann problem with Hardy-Littlewood-Sobolev nonlinearity
• A strongly indefinite Choquard equation with critical exponent due to the Hardy-Littlewood-Sobolev inequality