A Liouville-Type Theorem for the Lane-Emden Equation in a Half-space
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution that is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution that is bounded on finite strips. This question has a long history and our...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Oxford University Press
2022
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| Online Access: | View Fulltext in Publisher |
| Summary: | We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution that is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution that is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities. © 2021 The Author(s). |
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| ISBN: | 10737928 (ISSN) |
| DOI: | 10.1093/imrn/rnaa392 |