Symmetry and nonexistence of positive solutions for an elliptic system involving the Fractional Laplacian

DOI10.2989/16073606.2020.1854363zbMath1486.35453OpenAlexW3125656543MaRDI QIDQ5070213

Zuodong Yang, Rong Zhang, Xiaoshan Wang

Publication date: 11 April 2022

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2020.1854363

zbMATH Keywords

radially symmetric solutionsfractional LaplacianPohozaev identitymoving planessingularity estimates

Mathematics Subject Classification ID

Cauchy-Kovalevskaya theorems (35A10) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Axially symmetric solutions to PDEs (35B07)

Related Items (3)

Liouville-type theorem of positive periodic solutions for the periodic parabolic system ⋮ Nonexistence of anti-symmetric solutions for an elliptic system involving fractional Laplacian ⋮ Nonexistence of positive solutions for high-order Hardy-Hénon systems on \(\mathbb{R}^n\)

Cites Work

• Unnamed Item
• Fractional Laplacian: Pohozaev identity and nonexistence results
• Symmetry and nonexistence of positive solutions of integral systems with Hardy terms
• A direct method of moving planes for the fractional Laplacian
• The Pohozaev identity for the fractional Laplacian
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Symmetry and nonexistence of positive solutions for fractional systems
• On existence and nonexistence of positive solutions of an elliptic system with coupled terms
• A Pohozaev identity for the fractional Hénon system
• On the regularity of positive solutions of a class of Choquard type equations
• Super polyharmonic property of solutions for PDE systems and its applications
• Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space
• Definition of fractional Laplacian for functions with polynomial growth
• Liouville theorems involving the fractional Laplacian on a half space
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Fractional dynamics of systems with long-range interaction
• Homotopy perturbation method to fractional biological population equation
• A Liouville theorem for the higher-order fractional Laplacian
• Asymptotics of solutions of some nonlinear elliptic systems

This page was built for publication: Symmetry and nonexistence of positive solutions for an elliptic system involving the Fractional Laplacian