Comparison estimates on the first eigenvalue of a quasilinear elliptic system

完备黎曼流形上一类拟线性算子的非线性特征值问题

Nonlinear eigenvalue problems for a class of quasilinear operator on complete Riemannian manifolds

本文在Ricci曲率有下界的完备黎曼流形上研究一类拟线性算子的非线性特征值问题，推广Cheng--Yau梯度估计并证明非零特征值对应无界特征函数，同时将结果拓展到p-多孔介质方程等更一般的拟线性方程。

Nonsolvability of the asymptotic Dirichlet problems for some quasilinear elliptic PDEs on Hadamard manifolds

We show, by modifying Borbély's example, that there are $3$-dimen\-sional Cartan-Hadamard manifolds $M$, with sectional curvatures $\le -1$, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.

度量测度空间中拟线性椭圆方程的正则性

Regularity for quasilinear elliptic equations in metric measure spaces

本文利用 Galerkin 方法，证明了在 Ricci 曲率有下界的度量空间中拟线性椭圆方程的二阶与 Lipschitz 正则性，确立了 $p$-调和函数的 Lipschitz 正则性并证明了 Cheng-Yau 型不等式，超越了经典 Hölder 正则性理论。

On a class of quasilinear elliptic equation with indefinite weights on graphs

Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $Ω\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \left \{ \begin{array}{lcr} -Δ_{p}u= λK(x)|u|^{p-2}u+f(x,u), \ \ x\inΩ^{\circ}, u=0, \ \ x\in\partial Ω, \\ \end{array} \right. $$ where $Ω^{\circ}$ and $\partial Ω$ denote the interior and the boundary of $Ω$ respectively, $Δ_{p}$ is the discrete $p$-Laplacian, $K(x)$ is a given function which may change sign, $λ$ is the eigenvalue parameter and $f(x,u)$ has exponential growth. We pr…