Existence and multiplicity of solutions for Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity

DOI10.1016/j.aml.2019.01.017zbMath1416.35110OpenAlexW2914089788WikidataQ128585890 ScholiaQ128585890MaRDI QIDQ1739430

Shaoyun Shi, Yueqiang Song

Publication date: 26 April 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.01.017

zbMATH Keywords

mountain pass theoremKirchhoff equationconcentration-compactness principleHardy-Littlewood-Sobolev critical exponent

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60)

Related Items (7)

Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth ⋮ Existence to fractional critical equation with Hardy-Littlewood-Sobolev nonlinearities ⋮ Multiplicity of solutions for a class of Kirchhoff type equations with Hardy-Littlewood-Sobolev critical nonlinearity ⋮ Ground states solutions for a modified fractional Schrödinger equation with a generalized Choquard nonlinearity ⋮ Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term ⋮ On the \(p\)-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity ⋮ Fractional Kirchhoff-Choquard equation involving Schrödinger term and upper critical exponent

Cites Work

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• The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

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