A direct method of moving planes for the system of the fractional Laplacian

DOI10.2140/pjm.2017.290.301OpenAlexW2740444080MaRDI QIDQ2398624

Yingshu Lü, Chunxia Cheng, Zhong-Xue Lü

Publication date: 18 August 2017

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2017.290.301

zbMATH Keywords

method of moving planesradial symmetryfractional Laplaciannonexistence of positive solutionsnarrow region principledecay at infinitymaximum principles for antisymmetric functions

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (8)

Symmetry and nonexistence of solutions for a fully nonlinear nonlocal system ⋮ Classification of solutions to higher fractional order systems ⋮ On a super polyharmonic property of a higher-order fractional Laplacian ⋮ Maximum principles for Laplacian and fractional Laplacian with critical integrability ⋮ Symmetry of positive solutions for Lane-Emden systems involving the logarithmic Laplacian ⋮ Asymptotic method of moving planes for fractional parabolic equations ⋮ Symmetry for an integral system with general nonlinearity ⋮ Symmetry of positive solutions to quasilinear fractional systems

Cites Work

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• A direct method of moving planes for the fractional Laplacian
• The proof of the Lane-Emden conjecture in four space dimensions
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• Classification of solutions of some nonlinear elliptic equations
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• Indefinite fractional elliptic problem and Liouville theorems
• An Extension Problem Related to the Fractional Laplacian
• Symmetry via antisymmetric maximum principles in nonlocal problems of variable order

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