Symmetry and nonexistence of positive solutions to fractional \(p\)-Laplacian equations

DOI10.3934/DCDS.2019069zbMath1415.35286OpenAlexW2905296685MaRDI QIDQ1725813

Leyun Wu, Peng Cheng Niu

Publication date: 15 February 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019069

zbMATH Keywords

nonexistenceradial symmetryfractional \(p\)-Laplacian equationnarrow region principledirect method of moving planes

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (19)

Symmetry of solutions for a class of nonlocal Monge–Ampère equations ⋮ Symmetry of positive solutions to Choquard type equations involving the fractional \(p\)-Laplacian ⋮ Symmetry and monotonicity of positive solutions to Schrödinger systems with fractional \(p\)-Laplacians ⋮ Radial symmetry of a relativistic Schrödinger tempered fractional p-Laplacian model with logarithmic nonlinearity ⋮ Sliding method for fully nonlinear fractional order equations ⋮ Fractional \(p\)-Laplacian problems with negative powers in a ball or an exterior domain ⋮ Ancient solutions to nonlocal parabolic equations ⋮ Monotonicity and uniqueness of positive solutions to elliptic fractional \(p\)-equations ⋮ Monotonicity of positive solutions for fractional \(p\)-systems in unbounded Lipschitz domains ⋮ A direct method of moving planes for the fractional \(p\)-Laplacian system with negative powers ⋮ Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators ⋮ An anisotropic tempered fractional \(p\)-Laplacian model involving logarithmic nonlinearity ⋮ Monotonicity and symmetry of solutions to fractional \(p\)-Laplacian equations ⋮ Symmetry of positive solutions to quasilinear fractional systems ⋮ The sliding methods for the fractional \(p\)-Laplacian ⋮ Sliding methods for the higher order fractional Laplacians ⋮ Radial symmetry for a generalized nonlinear fractional p-Laplacian problem ⋮ Monotonicity and symmetry of solutions to fractional \(p\)-Laplacian systems ⋮ Monotonicity results for quasilinear fractional systems in epigraphs

Cites Work

• Radial symmetry results for fractional Laplacian systems
• The properties of positive solutions to an integral system involving Wolff potential
• A direct method of moving planes for the fractional Laplacian
• Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in \(\mathbb{R}^N\) involving fractional Laplacian
• Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
• Characterization of balls in terms of Bessel-potential integral equation
• A Liouville-type theorem for an integral equation on a half-space \(\mathbb R_+^n\)
• An overdetermined problem in Riesz-potential and fractional Laplacian
• Classification of positive solitary solutions of the nonlinear Choquard equation
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Maximum principles for the fractional p-Laplacian and symmetry of solutions
• Qualitative properties of solutions for an integral equation
• Positive solutions to nonlinear systems involving fully nonlinear fractional operators
• Asymptotic properties of positive solutions of the Hardy-Sobolev type equations
• Liouville theorems involving the fractional Laplacian on a half space
• Solutions of fully nonlinear nonlocal systems
• Indefinite fractional elliptic problem and Liouville theorems
• A concave—convex elliptic problem involving the fractional Laplacian
• Nonlocal Tug-of-War and the Infinity Fractional Laplacian
• Regularity theory for fully nonlinear integro-differential equations
• An Extension Problem Related to the Fractional Laplacian
• Classification of solutions for an integral equation
• Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

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