Gradient estimate for solutions of the equation Δ_p v+av^q=0 on a complete Riemannian manifold

2023/04/17 by He, Jie, Wang, Youde, Wei, Guodong · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.08238

Abstract

In this paper, we use Nash-Moser iteration method to study the local and global behaviours of positive solutions to the nonlinear elliptic equation Δ_pv +av^q=0 defined on a complete Riemannian manifolds (M,g) where p>1, a and q are constants. Under some assumptions on a, p and q, we derive gradient estimates and Liouville type theorems for such positive solutions.

Cited by

• Liouville theorem for the inequality Δ_m u+f(u)≤ 0 on Riemannian manifolds

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