A Liouville-type theorem for an integral equation on a half-space \(\mathbb R_+^n\)

DOI10.1016/j.jmaa.2012.01.015zbMath1241.45004OpenAlexW2055266228MaRDI QIDQ764977

Linfen Cao, Zhaohui Dai

Publication date: 16 March 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.01.015

zbMATH Keywords

symmetrymonotonicitymoving planes methodLiouville-type theorem

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (18)

Radial symmetry and monotonicity of solutions to a system involving fractional \(p\)-Laplacian in a ball ⋮ Liouville theorems for an integral system with Poisson kernel on the upper half space ⋮ Symmetry and monotonicity of positive solutions for a Choquard equation with the fractional Laplacian ⋮ Liouville type theorem to an integral system in the half-space ⋮ A Liouville-type theorem for an integral system on a half-space \(R_+^n\) ⋮ Super poly-harmonic property of solutions for Navier boundary problems on a half space ⋮ Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space ⋮ Liouville type theorems for a system of integral equations on upper half space ⋮ Symmetry and nonexistence of positive solutions for weighted HLS system of integral equations on a half space ⋮ Symmetry and nonexistence of positive solutions to fractional \(p\)-Laplacian equations ⋮ Liouville theorem for an integral system on the upper half space ⋮ Unnamed Item ⋮ Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space ⋮ Liouville-type theorem for some nonlinear systems in a half-space ⋮ An integral equation involving Bessel potentials on half space ⋮ The overdetermined equations on bounded domain ⋮ Nonexistence of positive solutions for an indefinite fractional \(p\)-Laplacian equation ⋮ Liouville type theorem for higher-order elliptic system with Navier boundary condition

Cites Work

• Unnamed Item
• Radial symmetry and regularity of solutions for poly-harmonic Dirichlet problems
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
• Classification of solutions of higher order conformally invariant equations
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Some nonexistence results for positive solutions of elliptic equations in unbounded domains.
• Uniqueness theorems through the method of moving spheres
• Existence results and a priori bounds for higher order elliptic equations and systems
• Liouville-type theorems for polyharmonic equations in $\mathbb{R}^N$ and in $\mathbb{R}^N_+$
• An integral equation on half space
• A priori bounds for positive solutions of nonlinear elliptic equations
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Non—existence of positive solutions to semilinear elliptic equations on r” or r” through the method of moving planes
• Uniqueness theorem for the entire positive solutions of biharmonic equations in Rⁿ
• Classification of solutions for an integral equation

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