Monotonicity and uniqueness of positive solutions to elliptic fractional \(p\)-equations

DOI10.1007/s13540-023-00136-5zbMath1511.35377OpenAlexW4360939764MaRDI QIDQ6045955

Pengyan Wang

Publication date: 15 May 2023

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13540-023-00136-5

zbMATH Keywords

monotonicityuniquenesssliding methodgradient termsparabolic inequalitieselliptic fractional \(p\)-equations

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92) Classical solutions to PDEs (35A09)

Cites Work

• A fractional Yamabe flow and some applications
• A direct method of moving planes for the fractional Laplacian
• Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
• Symmetry and related properties via the maximum principle
• Radial symmetry and monotonicity of solutions to a system involving fractional \(p\)-Laplacian in a ball
• Maximum principles for the fractional p-Laplacian and symmetry of solutions
• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• Symmetry and nonexistence of positive solutions to fractional \(p\)-Laplacian equations
• Sliding methods for the higher order fractional Laplacians
• Direct methods for pseudo-relativistic Schrödinger operators
• Monotonicity of solutions for fractional \(p\)-equations with a gradient term
• Hopf's lemmas for parabolic fractional \(p\)-Laplacians
• Symmetry and monotonicity of positive solutions for a system involving fractional p\&q-Laplacian in \(\mathbb{R}^n\)
• Maximum principles and monotonicity of solutions for fractional \(p\)-equations in unbounded domains
• Asymptotic method of moving planes for fractional parabolic equations
• The sliding methods for the fractional \(p\)-Laplacian
• Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations
• Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications
• Uniqueness and monotonicity of solutions for fractional equations with a gradient term
• Monotonicity and symmetry of positive solutions to fractional p-Laplacian equation
• On the method of moving planes and the sliding method

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