On the classification of solutions of $-\Delta u= e^u$ on $\mathbb {R}^N$: Stability outside a compact set and applications
On the classification of solutions of $-\Delta u= e^u$ on $\mathbb {R}^N$: Stability outside a compact set and applications
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DOI：
10.1090/s0002-9939-08-09772-4
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
E. N. Dancer;A. Farina
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文献类型：
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作者：
E. N. Dancer;A. Farina
在这篇短文中，我们证明了对于3<；N<；9，整个欧氏空间RN上的问题-Δu=eu不允许在RN的紧集之外稳定的任何解。这一结果是在不对解的有界性做任何假设的情况下得到的。此外，作为分析的结果，我们还证明了所考虑问题的有限Morse指数解的不存在性。然后利用我们的结果给出了有界域问题的一些应用。
In this short paper we prove that, for 3 < N < 9, the problem -Δu = e u on the entire Euclidean space R N does not admit any solution stable outside a compact set of R N . This result is obtained without making any assumption about the boundedness of solutions. Furthermore, as a consequence of our analysis, we also prove the non-existence of finite Morse Index solutions for the considered problem. We then use our results to give some applications to bounded domain problems.