论文标题
具有指数非线性的Hénon类型方程的定性特性
Qualitative properties of Hénon type equations with exponential nonlinearity
论文作者
论文摘要
我们对具有指数非线性的Hénon类型方程解决方案的定性属性感兴趣。首先，我们对$ΔU +| x | x |^αe^u = 0 $ in $ \ mathbb {r}^n $ in Infinity Solutions进行分类，该$ = 0 $，这给了[Wang-Ye]中考虑的问题。其次，获得了整个径向溶液对$δ^2 u = | x |^αe^u $的存在和精确的渐近行为。然后，我们将无限径向溶液的稳定和稳定分类为$δ^2 u = | x |^αe^u $在任何维度上。
We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of $Δu +|x|^αe^u=0$ in $\mathbb{R}^N$, which gives a complete answer to the problem considered in [Wang-Ye]. Secondly, existence and precise asymptotic behaviors of entire radial solutions to $Δ^2 u=|x|^α e^u$ are obtained. Then we classify the stable and stable at infinity radial solutions to $Δ^2 u=|x|^α e^u$ in any dimension.
