Liouville type theorems of a nonlinear elliptic equation for the \(V\)-Laplacian

DOI10.1007/S13324-017-0168-6zbMath1390.35059OpenAlexW2592537700MaRDI QIDQ1743911

Guangyue Huang, Zhi Li

Publication date: 16 April 2018

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

Full work available at URL: https://doi.org/10.1007/s13324-017-0168-6

zbMATH Keywords

positive solutionsLiouville-type theoremsBakry-Émry-Ricci curvature

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Positive solutions to PDEs (35B09) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (11)

Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation ⋮ Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds ⋮ Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian on noncompact Riemannian manifolds ⋮ Gradient estimations for nonlinear elliptic equations on weighted Riemannian manifolds ⋮ Weighted Sobolev type inequalities in a smooth metric measure space ⋮ Unnamed Item ⋮ Gradient estimates and Liouville type theorems for \((p-1)^{p-1}\Delta_pu+au^{p-1}\log u^{p-1}=0\) on Riemannian manifolds ⋮ Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds ⋮ Gradient estimates of a nonlinear elliptic equation for the \(V\)-Laplacian ⋮ Gradient and Hessian estimates for an elliptic equation on smooth metric measure spaces ⋮ Gradient estimates for a weighted nonlinear elliptic equation and Liouville type theorems

Cites Work

• Unnamed Item
• A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry
• Gradient estimates and Harnack inequalities of a nonlinear parabolic equation for the \(V\)-Laplacian
• Li-Yau-Hamilton estimates and Bakry-Emery-Ricci curvature
• Existence and Liouville theorems for \(V\)-harmonic maps from complete manifolds
• Comparison geometry for the Bakry-Emery Ricci tensor
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• Li-Yau type estimates for a nonlinear parabolic equation on complete manifolds
• Gradient estimates and differential Harnack inequalities for a nonlinear parabolic equation on Riemannian manifolds
• A Liouville-type theorem for smooth metric measure spaces
• Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds
• Harmonic functions on complete riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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