论文标题
具有梯度术语的K-Hessian类型方程的整个亚物业
Entire subsolutions of a kind of k-Hessian type equations with gradient terms
论文作者
论文摘要
在本文中，我们考虑了一种$ k $ -Hessian类型方程$ s_k^{\ frac {\ frac {1} {k}}（d^2u+μ| d u | i）= f（u）$ in $ \ m athbb {r}^n $，并提供$ f $的必要和不合时宜的条件。凯勒·塞曼（Keller-Sosserman）条件。存在和不存在的结果分别以参数$μ$的不同范围证明，这是JI和BAO（Proc Amer Math Soc 138：175--188，2010）的标准Hessian方程式案例（$μ= 0 $）。半线性案例（$ k = 1 $）和完全非线性案例（$ k \ ge 2 $）之间的差异也是如此。
In this paper, we consider a kind of $k$-Hessian type equations $S_k^{\frac{1}{k}}(D^2u+μ|D u|I)= f(u)$ in $\mathbb{R}^n$, and provide a necessary and sufficient condition of $f$ on the existence and nonexistence of entire admissible subsolutions, which can be regarded as a generalized Keller-Osserman condition. The existence and nonexistence results are proved in different ranges of the parameter $μ$ respectively, which embrace the standard Hessian equation case ($μ=0$) by Ji and Bao (Proc Amer Math Soc 138: 175--188, 2010) as a typical example. The difference between the semilinear case ($k=1$) and the fully nonlinear case ($k\ge 2$) is also concerned.
