Liouville theorem and classification of positive solutions for a fractional Choquard type equation

DOI10.1016/j.na.2019.03.006zbMath1419.35216OpenAlexW2923219718WikidataQ128198117 ScholiaQ128198117MaRDI QIDQ2312560

Yanyan Li

Publication date: 17 July 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2019.03.006

zbMATH Keywords

Liouville theoremsfractional Choquard equationsclassification of positive solutions

Mathematics Subject Classification ID

Fractional partial differential equations (35R11)

Related Items (23)

Symmetry of positive solutions to Choquard type equations involving the fractional \(p\)-Laplacian ⋮ Symmetry and monotonicity of positive solutions for a Choquard equation with the fractional Laplacian ⋮ Integrability of solutions for the integral system ⋮ Fractional \(p\)-Laplacian problems with negative powers in a ball or an exterior domain ⋮ Uniqueness of non-negative solutions to an integral equation of the Choquard type ⋮ Liouville theorems for Hénon type Choquard equation ⋮ Liouville‐type theorems for a nonlinear fractional Choquard equation ⋮ Classical solutions to a Hartree type system ⋮ A nonexistence result for the Choquard-type Hamiltonian system ⋮ Asymptotic decay of solutions for sublinear fractional Choquard equations ⋮ Liouville theorem and qualitative properties of solutions for an integral system ⋮ Symmetry of solutions for a fractional p-Laplacian equation of Choquard type ⋮ On Liouville theorems of a Hartree–Poisson system ⋮ Bound states of fractional Choquard equations with Hardy-Littlewood-Sobolev critical exponent ⋮ Symmetry and nonexistence results for a fractional Choquard equation with weights ⋮ Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction ⋮ Symmetry of positive solutions to quasilinear fractional systems ⋮ Bound state solutions of fractional Choquard equation with Hardy-Littlewood-Sobolev critical exponent ⋮ Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order ⋮ Symmetry and classification of solutions to an integral equation of the Choquard type ⋮ Liouville theorems for an integral equation of Choquard type ⋮ Multiple bound state solutions for fractional Choquard equation with Hardy–Littlewood–Sobolev critical exponent ⋮ On classical solutions to the Hartree equation

Cites Work

• A direct method of moving planes for the fractional Laplacian
• A guide to the Choquard equation
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Classification of positive solitary solutions of the nonlinear Choquard equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Regularity, symmetry, and uniqueness of some integral type quasilinear equations
• Remarks about a fractional Choquard equation: ground state, regularity and polynomial decay
• Existence and multiplicity of solutions for fractional Choquard equations
• Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes
• Nodal solutions for a fractional Choquard equation
• Liouville theorems and classification results for a nonlocal Schrödinger equation
• On gravity's role in quantum state reduction
• Classification of positive solutions for a static Schrödinger-Maxwell equation with fractional Laplacian
• Fractional dynamics of systems with long-range interaction
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Variational Methods for Nonlocal Fractional Problems
• Euler Equations, Navier-Stokes Equations and Turbulence
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• On fractional Choquard equations
• Classification of solutions for an integral equation
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