A Liouville theorem for \(\alpha\)-harmonic functions in \(\mathbb{R}^n_+\)

DOI10.3934/dcds.2016.36.1721zbMath1338.35461arXiv1409.4106OpenAlexW2963589211MaRDI QIDQ256193

Wenxiong Chen, Congming Li, Tingzhi Cheng, Li-Zhi Zhang

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1409.4106

zbMATH Keywords

Liouville theoremuniqueness of solutionsfractional Laplacian\(\alpha\)-harmonic functionsPoisson representation

Mathematics Subject Classification ID

Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications, Liouville type theorems for the system of fractional nonlinear equations in \(\mathbb R^n_+\), Property of solutions for elliptic equation involving the higher-order fractional Laplacian in \(\mathbb{R}^n_+\), Liouville theorem for poly-harmonic functions on \(\mathbb{R}^n_+ \), Liouville type theorem for higher order Hénon equations on a half space, Maximum principles involving the uniformly elliptic nonlocal operator, The maximum principles for fractional Laplacian equations and their applications, Direct methods on fractional equations, A priori bounds and existence result of positive solutions for fractional Laplacian systems, Symmetry properties in systems of fractional Laplacian equations, Liouville type theorems for PDE and IE systems involving fractional Laplacian on a half space, A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\), A Liouville theorem for Lévy generators, Liouville theorem for fractional Hénon–Lane–Emden systems on a half space, Nonlinear elliptic systems involving the fractional Laplacian in the unit ball and on a half space, Symmetry of solutions to semilinear equations involving the fractional Laplacian, Liouville theorems for nonnegative solutions to Hardy-Hénon type system on a half space, Radial symmetry for systems of fractional Laplacian

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