论文标题
$ΔU + au（\ log u）^{p} + bu = 0 $ in Riemannian歧管上的YAU类型梯度估计值
Yau Type Gradient Estimates For $Δu + au(\log u)^{p}+bu=0$ On Riemannian Manifolds
论文作者
论文摘要
在本文中，我们考虑了在完整的Riemannian歧管$（m，g）$ $ $ $ $ $ $Δu + au（\ log u）^{p} + bu = 0，$ a，$ a，b \ in \ mathbb {r} $和$ p $中是有理编号$ p = \ frac {k_1} {2k_2+1} \ geq2 $其中$ k_1 $和$ k_2 $是正整数。我们获得了与方程式的阳性解的梯度界限，该方程不取决于解决方案的边界和距离函数的拉普拉斯（Laplacian）在$（m，g）$上。我们的结果可以看作是Yau对正谐波功能的估计的自然扩展。
In this paper, we consider the gradient estimates of the positive solutions to the following equation defined on a complete Riemannian manifold $(M, g)$ $$Δu + au(\log u)^{p}+bu=0,$$ where $a, b\in \mathbb{R}$ and $p$ is a rational number with $p=\frac{k_1}{2k_2+1}\geq2$ where $k_1$ and $k_2$ are positive integer numbers. we obtain the gradient bound of a positive solution to the equation which does not depend on the bounds of the solution and the Laplacian of the distance function on $(M, g)$. Our results can be viewed as a natural extension of Yau's estimates on positive harmonic function.
