| Autor: |
Guo, Zongming, Huang, Xia, Ye, Dong, Zhou, Feng |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Nonlinearity 35 (2022) 492-512 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1361-6544/ac3925 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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