5 papers · 1 filter
Liouville theorem of the subcritical biharmonic equation on complete manifolds
Xi-Nan Ma, Tian Wu, Wangzhe Wu
In this paper, we study the subcritical biharmonic equation \[Δ^2 u=u^α\] on a complete, connected, and non-compact Riemannian manifold with nonnegative Ricci curvature.…
The Liouville-type equation and an Onofri-type inequality on closed 4-manifolds
Xi-Nan Ma, Tian Wu, Xiao Zhou
In this paper, we study the Liouville-type equation \[Δ^2 u-λ_1κΔu+λ_2κ^2(1-\mathrm e^{4u})=0\] on a closed Riemannian manifold \((M^4,g)\) with \(\operatorname{Ric}\geqslant 3κg\)…
Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities
Daowen Lin, Xi-Nan Ma
We derive an integral identity for a class -Laplace equation, and then classify all positive finite energy cylindrically symmetric solutions of the equation (\ref{1.2}) for $3\l…
The Dirichlet problem of homogeneous complex k-Hessian equation in a (k-1)-pesudoconvex domain with isolated singularity
Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the homogeneous complex k-Hessian equation in . We prove the existence and uniqueness of the solution by constructing approxi…
The Dirichlet problem of the homogeneous -Hessian equation in a punctured domain
Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the Dirichlet problem for the homogeneous -Hessian equation with prescribed asymptotic behavior at where is a -convex bounded domai…