论文标题
$ K $ -Hessian方程的半稳定径向解决方案的一些结果
Some results for semi-stable radial solutions of $k$-Hessian equations
论文作者
论文摘要
我们将本文用于研究$ s_k（d^2u）= w（| x |）g（u）$ $ s_k（d^2u）$ r^n $的半稳定非径向解决方案。我们建立了该方程中存在此类解决方案（不一定是有限的）的点上估计和必要条件。对于有限的解决方案，我们估计它们在无穷大的渐近行为。所有估计都根据空间尺寸$ n $，$ k $的值以及无限的行为的增长率函数的行为给出。
We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u) = w(|x|)g(u)$ on the Euclidean space $R^n$. We establish pointwise estimates and necessary conditions for the existence of such solutions (not necessarily bounded) for this equation. For bounded solutions we estimate their asymptotic behavior at infinity. All the estimates are given in terms of the spatial dimension $n$, the values of $k$ and the behavior at infinity of the growth rate function of $w$.
