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On the classification of solutions of -Δ𝑢=𝑒^{𝑢} on ℝ^{ℕ}: Stability outside a compact set and applications
- Source :
- Proceedings of the American Mathematical Society. 137:1333-1338
- Publication Year :
- 2008
- Publisher :
- American Mathematical Society (AMS), 2008.
-
Abstract
- In this short paper we prove that, for3≤N≤93 \le N \le 9, the problem−Δu=eu-\Delta u = e^uon the entire Euclidean spaceRN\mathbb {R}^Ndoes not admit any solution stable outside a compact set ofRN\mathbb {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.
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 137
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi...........534fe89f3340322d03114304f6792c91