Jie He

collaborators

5 papers

math.AP2024

Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds

Jie He, Linlin Sun, Youde Wang

We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of p…

math.AP2024

Local and Global Log-Gradient estimates of solutions to $Δ_{p} v + b v^{q} + c v^{r} = 0$ on manifolds and applications

Jie He, Yuanqing Ma, Youde Wang

In this paper, we employ the Nash-Moser iteration technique to study local and global properties of positive solutions to the equation $Δ_{p} v + b v^{q} + c v^{r} = 0$ on complete Riemannian…

math.AP2023

On the universal local and global properties of positive solutions to $Δ_{p} v + b ∣\nabla v ∣^{q} + c v^{r} = 0$ on complete Riemannian manifolds

Jie He, Youde Wang

In this paper we study the positive solutions to a nonlinear elliptic equation $Δ_{p} v + b ∣\nabla v ∣^{q} + c v^{r} = 0$ defined on a complete Riemannian manifold $(M, g)$ with Ricci curvature…

math.AP2023

Nash-Moser iteration approach to the logarithmic gradient estimates and Liouville Properties of quasilinear elliptic equations on manifolds

Jie He, Jingchen Hu, Youde Wang

In this paper, we provide a new routine to employ the Nash-Moser iteration technique to analyze the local and global properties of positive solutions to the equation $$Δ_pv + a|\na…

math.AP2023

Gradient estimates for $Δ_{p} u - ∣\nabla u ∣^{q} + b (x) ∣ u ∣^{r - 1} u = 0$ on a complete Riemannian manifold and Liouville type theorems

Dong Han, Jie He, Youde Wang

In this paper the Nash-Moser iteration method is used to study the gradient estimates of solutions to the quasilinear elliptic equation $Δ_{p} u - ∣\nabla u ∣^{q} + b (x) ∣ u ∣^{r - 1} u = 0$ define…

Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds

Local and Global Log-Gradient estimates of solutions to Δp​v+bvq+cvr=0 on manifolds and applications

On the universal local and global properties of positive solutions to Δp​v+b∣∇v∣q+cvr=0 on complete Riemannian manifolds

Nash-Moser iteration approach to the logarithmic gradient estimates and Liouville Properties of quasilinear elliptic equations on manifolds

Gradient estimates for Δp​u−∣∇u∣q+b(x)∣u∣r−1u=0 on a complete Riemannian manifold and Liouville type theorems

Local and Global Log-Gradient estimates of solutions to $Δ_{p} v + b v^{q} + c v^{r} = 0$ on manifolds and applications

On the universal local and global properties of positive solutions to $Δ_{p} v + b ∣\nabla v ∣^{q} + c v^{r} = 0$ on complete Riemannian manifolds

Gradient estimates for $Δ_{p} u - ∣\nabla u ∣^{q} + b (x) ∣ u ∣^{r - 1} u = 0$ on a complete Riemannian manifold and Liouville type theorems