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arXiv · 2012.13531

Qualitative properties of H\'enon type equations with exponential nonlinearity

Zongming Guo·Xia Huang·Dong Ye·Feng Zhou
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Abstract

We are interested in the qualitative properties of solutions of the H\'enon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of $\Delta u +|x|^\alpha e^u=0$ 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 $\Delta^2 u=|x|^{\alpha} e^u$ are obtained. Then we classify the stable and stable at infinity radial solutions to $\Delta^2 u=|x|^{\alpha} e^u$ in any dimension.

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Zongming Guo, Xia Huang, Dong Ye, Feng Zhou. 2020-12-25. Qualitative properties of H\'enon type equations with exponential nonlinearity. https://doi.org/10.1088/1361-6544/ac3925

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