A constructive approach to positive solutions of \(\delta_pu+f(u,u)\) on Riemannian manifolds

DOI10.1016/J.ANIHPC.2015.06.003zbMath1353.58009OpenAlexW1005104753WikidataQ115360610 ScholiaQ115360610MaRDI QIDQ342592

Jie Xiao, Yu-Zhao Wang

Publication date: 17 November 2016

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2015.06.003

zbMATH Keywords

complete Riemannian manifoldnon-negative solutionvolume growth consideration

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Elliptic equations on manifolds, general theory (58J05) PDEs on manifolds (35R01)

Related Items (9)

Liouville type theorems for systems of elliptic differential inequalities on Riemannian manifolds ⋮ Absence of nonnegative solutions to the system of differential inequalities on manifolds ⋮ Nonnegative solutions of a fractional differential inequality on Grushin spaces and nilpotent Lie groups ⋮ Quasilinear Laplace equations and inequalities with fractional orders ⋮ Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold ⋮ A sharp Liouville principle for \(\Delta_m u+u^p|\nabla u|^q\le 0\) on geodesically complete noncompact Riemannian manifolds ⋮ On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds ⋮ Absence of positive solutions to the system of differential inequalities on manifolds ⋮ The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain

Cites Work

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• On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds
• On sufficient conditions for the existence of radially symmetric solutions of the \(p\)-Laplace equation
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Differential equations on riemannian manifolds and their geometric applications
• On Nonnegative Solutions of the Inequality Δ u + u^σ ≤ 0 on Riemannian Manifolds

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