11 papers
Liouville type theorems for some -Laplace equations with gradient dependent reaction on Riemannian manifolds
Youde Wang, Liqin Zhang
In this paper, we combine Bochner formula, Saloff-Coste's Sobolev inequality and the Nash-Moser iteration method to study the local and global behaviors of solutions to the nonline…
Quasi-linear equation on manifolds with integral bounded Ricci curvature and geometric applications
Youde Wang, Guodong Wei, Liqin Zhang
We study nonexistence results and gradient estimates for solutions of \[ Δ_p v + a v^{q}=0 \] defined on complete Riemannian manifolds satisfying a \emph{-type Sobolev inequalit…
Liouville theorems and new gradient estimates for positive solutions to on a complete manifold
Youde Wang, Linqin Zhang
In this paper, we use the Saloff-Coste Sobolev inequality and Nash-Moser iteration method to study the local and global behaviors of positive solutions to the nonlinear elliptic eq…
Cheng-Yau logarithmic gradient estimates for a nonlinear elliptic equation on smooth metric measure spaces
Cheng Jin, Youde Wang, Fanqi Zeng
In this paper, we consider the nonlinear elliptic equation on a complete smooth metric measure space with -Bakry-Émery Ricci curvature bounded from below, where…
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…
Local and Global Log-Gradient estimates of solutions to 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 on complete Riemannian…