A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\)

DOI10.1016/J.JDE.2017.07.009zbMath1396.35081arXiv1611.09133OpenAlexW2737835237MaRDI QIDQ1785951

Mei Yu, Jianming He, Li-Zhi Zhang

Publication date: 2 October 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09133

zbMATH Keywords

Liouville theoremnarrow region principledecay at infinitythe fractional LaplacianA direct method of moving planes

Mathematics Subject Classification ID

Boundary value problems for PDEs with pseudodifferential operators (35S15) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (12)

Symmetry and nonexistence of solutions for a fully nonlinear nonlocal system ⋮ Liouville type theorem for fractional Laplacian system ⋮ Fractional \(p\)-Laplacian problems with negative powers in a ball or an exterior domain ⋮ Property of solutions for elliptic equation involving the higher-order fractional Laplacian in \(\mathbb{R}^n_+\) ⋮ Existence of positive solutions to a fractional-Kirchhoff system ⋮ Symmetry of solutions for a fractional p-Laplacian equation of Choquard type ⋮ Liouville theorem for fractional Hénon–Lane–Emden systems on a half space ⋮ Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space ⋮ A priori bounds and existence of positive solutions for fractional Kirchhoff equations ⋮ On positive viscosity solutions of fractional Lane-Emden systems ⋮ Monotonicity results for quasilinear fractional systems in epigraphs ⋮ Liouville type theorem for a singular elliptic equation with finite Morse index

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